Manuel Ojeda-Aciego's publications

[247]
N. Madrid, J. Medina, M. Ojeda-Aciego, and I. Perfilieva. L-fuzzy relational mathematical morphology based on adjoint triples. Information Sciences, 474:75-89, 2019. [ bib | DOI | .pdf ]
We propose an alternative to the standard structure of L-fuzzy Mathematical Morphology (MM) by, on the one hand, considering L-fuzzy relations as structuring elements and, on the other hand, by using adjoint triples to handle membership values. Those modifications lead to a framework based on set-theoretical operations where we can prove a representation theorem for algebraic morphological erosions and dilations. In addition, we also present some new results concerning duality and transformation invariance. Concerning duality, we show that duality and adjointness can coexist in this L-fuzzy relational MM. Concerning transformation invariance, we show sufficient conditions to guarantee the invariance of morphological operators under arbitrary transformations.

[246]
O. Krídlo and M. Ojeda-Aciego. Relating Hilbert-Chu correspondences and big toy models for quantum mechanics. In Proc. of Eur. Symp. on Computational Intelligence and Mathematics (ESCIM 2018), 2018. To appear. [ bib ]
[245]
I.P. Cabrera, P. Cordero, E. Muñoz Velasco, and M. Ojeda-Aciego. Relational connections between preordered sets. In Proc. of Applied Physics, System Science and Computers (APSAC 2018), 2018. To appear. [ bib ]
[244]
I.P. Cabrera, P. Cordero, E. Muñoz Velasco, and M. Ojeda-Aciego. Compatibility of Galois connections and powering. In Proc. of the Computational and Mathematical Methods in Science and Engineering, CMMSE'18, 2018. [ bib ]
[243]
A. Burrieza, E. Muñoz Velasco, and M. Ojeda-Aciego. A flexible logic-based approach to closeness using order of magnitude qualitative reasoning. Logic Journal of the IGPL, 2018. To appear. [ bib | .pdf ]
In this paper, we focus on a logical approach to the important notion of closeness, which has not received much attention in the literature. Our notion of closeness is based on the so-called proximity intervals, which will be used to decide the elements that are close to each other. Some of the intuitions of this definition are explained on the basis of examples. We prove the decidability of the recently introduced multimodal logic for closeness and, then, we show some capabilities of the logic with respect to expressivity in order to denote particular positions of the proximity intervals.

[242]
J. Medina, M. Ojeda-Aciego, J.L. Verdegay, D. Pelta, I.P. Cabrera, B. Bouchon-Meunier, and R. Yager, editors. Information Processing and Management of Uncertainty in Knowledge-Based Systems: Theory and Foundations I, volume 853 of Communications in Computer and Information Science. Springer, 2018. [ bib | DOI ]
[241]
J. Medina, M. Ojeda-Aciego, J.L. Verdegay, D. Pelta, I.P. Cabrera, B. Bouchon-Meunier, and R. Yager, editors. Information Processing and Management of Uncertainty in Knowledge-Based Systems: Theory and Foundations II, volume 854 of Communications in Computer and Information Science. Springer, 2018. [ bib | DOI ]
[240]
J. Medina, M. Ojeda-Aciego, J.L. Verdegay, I. Perfilieva, B. Bouchon-Meunier, and R. Yager, editors. Information Processing and Management of Uncertainty in Knowledge-Based Systems: Applications, volume 855 of Communications in Computer and Information Science. Springer, 2018. [ bib | DOI ]
[239]
F. Valverde-Albacete, C. Peláez-Moreno, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. A data analysis application of formal independence analysis. In Proc. of the Intl Conf on Concept Lattices and their Applications, CLA'18, pages 117-128, 2018. [ bib | .pdf ]
In this paper we present a new technique for the analysis of data tables by means of Formal Independence Analysis (FIA). This is an analogue of Formal Concept Analysis for the study of independence relations in data, instead of hierarchical relations. A FIA of a context produces, when possible, its block diagonalization by detecting pairs of sets of objects and attributes that are not mutually incident, or tomoi, that partition the context. In this paper we combine this technique with the exploration of contexts with entries in a semifield to find independent sets in contingency matrices. Specifically, we apply it to a number of confusion matrices issued from cognitive experiments to find evidences for the hypothesis of perceptual channels.

[238]
A. Burrieza, E. Muñoz-Velasco, and M. Ojeda-Aciego. Logics for order-of-magnitude qualitative reasoning: formalizing negligibility. In M. Zawidzki and J. Golińska-Pilarek, editors, Ewa Orlowska on Relational Methods in Logic and Computer Science, Outstanding Contributions to Logic, chapter 8. Springer, 2018. To appear. [ bib ]
Qualitative reasoning deals with information expressed in terms of qualitative classes and relations among them, such as comparability, negligibility or closeness. In this work, we focus on the different logic-based approaches to the notions of negligibility developed by our group.

[237]
O. Krídlo and M. Ojeda-Aciego. Formal concept analysis and structures underlying quantum logics. Communications in Computer and Information Science, 853:574-584, 2018. [ bib | .pdf ]
A Hilbert space H induces a formal context, the Hilbert formal context, whose associated concept lattice is isomorphic to the lattice of closed subspaces of H. This set of closed subspaces, denoted C(H), is important in the development of quantum logic and, as an algebraic structure, corresponds to a so-called “propositional system”, that is, a complete, atomistic, orthomodular lattice which satisfies the covering law. In this paper, we continue with our study of the Chu construction by introducing the Chu correspondences between Hilbert contexts, and showing that the category of Propositional Systems, PropSys, is equivalent to the category of Chu correspondences between Hilbert contexts.

[236]
F. Valverde-Albacete, C. Peláez-Moreno, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Formal independence analysis. Communications in Computer and Information Science, 853:596-608, 2018. [ bib | .pdf ]
In this paper we propose a new lens through which to observe the information contained in a formal context. Instead of focusing on the hierarchical relation between objects or attributes induced by their incidence, we focus on the “unrelatedness” of the objects with respect to those attributes with which they are not incident. The crucial order concept for this is that of maximal anti-chain and the corresponding representation capabilities are provided by Behrendt's theorem. With these tools we introduce the fundamental theorem of Formal Independence Analysis and use it to provide an example of what its affordances are for the analysis of data tables. We also discuss its relation to Formal Concept Analysis.

[235]
I.P. Cabrera, P. Cordero, F. Garcia-Pardo, M. Ojeda-Aciego, and B. De Baets. Galois connections between a fuzzy preordered structure and a general fuzzy structure. IEEE Transactions on Fuzzy Systems, 26(3):1274-1287, 2018. [ bib | DOI | .pdf ]
We continue the study of (isotone) Galois connections, also called adjunctions, in the framework of fuzzy preordered structures, which generalize fuzzy preposets by considering underlying fuzzy equivalence relations. Specifically, we present necessary and sufficient conditions so that, given a mapping f: A -> B from a fuzzy preordered structure A into a fuzzy structure B, it is possible to construct a fuzzy relation rho_B that induces a suitable fuzzy preorder structure on B and such that there exists a mapping g: B ->A such that the pair (f,g) constitutes an Galois connection..

[234]
N. Madrid and M. Ojeda-Aciego. Inconsistency measures in general fuzzy logic programming. In J. Grant and M.V. Martinez, editors, Measuring Inconsistency in Information, volume 73 of Studies in Logic, chapter 5, pages 147-168. College publications, 2018. [ bib | http ]
Fuzzy logic  has shown to be a suitable framework to handle contradictions in which, unsurprisingly,  the notion of inconsistency can be defined in different ways. This chapter analyses the notion of inconsistency in general residuated logic programming under the answer-set semantics, shows that inconsistency can be somehow decomposed into instability and incoherence and, finally, shows that each of these notions can be associated with some natural measures of inconsistency. Finally, we focus on measures of inconsistency in the particular framework of fuzzy logic programming.

[233]
H. Bustince, S. Montes, and M. Ojeda-Aciego. Fuzzy mathematical models for computer science and decision making. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 25:1-4, 2017. [ bib | DOI ]

[232]
A. Burrieza, E. Muñoz Velasco, and M. Ojeda-Aciego. A multimodal logic for closeness. Journal of Applied Non-Classical Logics, 27:225-237, 2017. [ bib | DOI | .pdf ]
We introduce a multimodal logic for order of magnitude reasoning which considers a new logic-based alternative to the notion of closeness, we provide an axiom system and prove its soundness and completeness.

[231]
O. Krídlo and M. Ojeda-Aciego. An adjoint pair for intuitionistic L-fuzzy values. In Proc. of the European Symposium on Computational Intelligence and Mathematics ESCIM'17, 2017. To appear. [ bib | .pdf ]
We continue our prospective study of the generalization of formal concept analysis in terms of intuitionistic L-fuzzy sets. The main contribution here is an adjoint pair in the set Li of intuitionistic L-fuzzy values associated to a complete residuated lattice, which allows the definition of a pair of derivation operators which form an antitone Galois connection.

[230]
I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Relation-based Galois connections: towards the residual of a relation. In Computational and Mathematical Methods in Science and Engineering (CMMSE'17), 2017. [ bib | .pdf ]
We explore a suitable generalization of the notion of Galois connection in which their components are binary relations. Many different approaches are possible depending both on the (pre-)order relation between subsets in the underlying powerdomain and the chosen type of relational composition.

[229]
I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Galois connections in computational intelligence: a short survey. In Foundations of Computational Intelligence (FOCI@SSCI'17), 2017. [ bib | DOI | .pdf ]
The construction of Galois connections between different structures provides a number of advantages, both from the theoretical and the applied standpoints. In this paper, we survey some works on Galois connections focused essentially on certain aspects of Computational Intelligence.

[228]
N. Madrid and M. Ojeda-Aciego. Modelling fuzzy partitions with fuzzy answer sets. In Foundations of Computational Intelligence (FOCI@SSCI'17), 2017. [ bib | DOI | .pdf ]
This paper introduces a representation of fuzzy partitions in term of fuzzy logic programming. This representation models relationships among the different classes that define the fuzzy partition. There are essentially two such relationships. The first one is that classes are disjoint and, therefore, contradictory each other; on the other hand, the second one is that classes cover all the universe. These two relationships are modeled via two different negations, namely, the explicit and default negation. Last but not least, the semantics used to model both negations is the fuzzy answer set semantics.

[227]
N. Madrid and M. Ojeda-Aciego. A view of f-indexes of inclusion under different axiomatic definitions of fuzzy inclusion. Lecture Notes in Artificial Intelligence Science, 10564:307-318, 2017. [ bib | DOI | .pdf ]
In this paper we analyze the novel constructive definition of f-index of inclusion with respect to four of the most common axiomatic definitions of inclusion measure, namely Sinha-Dougherty, Kitainik, Young and Fan-Xie-Pei. There exist an important difference between the f-index and these axiomatic definitions of inclusion measure: the f-index represents the inclusion in terms of a mapping in unit interval, whereas the inclusion measure represents such an inclusion as a value in the unit interval.

[226]
I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Relational fuzzy Galois connections. In Joint 17th World Congress of Intl Fuzzy Systems Association and 9th Intl Conf on Soft Computing and Intelligent Systems (IFSA-SCIS'17), 2017. [ bib | DOI | .pdf ]
We propose a suitable generalization of the notion of Galois connection whose components are fuzzy relations. We prove that the construction embeds Yao's notion of fuzzy Galois connection as a particular case. Although the natural framework for the proposed notion is that of fuzzy preposets, we also prove that it behaves properly with respect to the formation of quotient with respect to the fuzzy symmetric kernel relation.

[225]
O. Krídlo and M. Ojeda-Aciego. Towards intuitionistic L-fuzzy formal t-concepts. In Joint 17th World Congress of Intl Fuzzy Systems Association and 9th Intl Conf on Soft Computing and Intelligent Systems (IFSA-SCIS'17), 2017. [ bib | DOI | .pdf ]
We continue our study of intuitionistic L-fuzzy formal concept analysis by presenting a construction of an adjoint triple based on a non-commutative conjunctor, so that it enables the construction of intuitionistic L-fuzzy t-formal concepts.

[224]
I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Towards relational fuzzy adjunctions. In IEEE Intl Conf on Fuzzy Systems (FUZZ-IEEE'17), 2017. [ bib | DOI | .pdf ]
The problem of studying the existence of a right adjoint for a mapping defined between sets with different fuzzy structure naturally leads to the search of new notions of adjunction which fit better with the underlying structure of domain and codomain. In this work, we introduce a version of relational fuzzy adjunction between fuzzy preposets which generalizes previous approaches in that its components are fuzzy relations. We also prove that the construction behaves properly with respect to the formation of quotient with respect to the symmetric kernel relation and, thus, giving rise to a relational fuzzy adjunction between fuzzy posets.

[223]
O. Krídlo and M. Ojeda-Aciego. Extending formal concept analysis using intuitionistic L-fuzzy sets. In IEEE Intl Conf on Fuzzy Systems (FUZZ-IEEE'17), 2017. [ bib | DOI | .pdf ]
A two-fold general approach to the theory of formal concept analysis is introduced by considering intuitionistic fuzzy sets valued on a residuated lattice as underlying structure for the construction.

[222]
L. Antoni, I. P. Cabrera, S. Krajči, O. Krídlo, and M. Ojeda-Aciego. The Chu construction and generalized formal concept analysis. Intl J of General Systems, 46:458-474, 2017. [ bib | DOI | .pdf ]
We continue studying the connections between the Chu construction on the category ChuCors of formal contexts and Chu correspondences, and generalizations of Formal Concept Analysis (FCA). All the required constructions like categorical product, tensor product, together with its bifunctor properties are introduced and proved. The final section focuses on how the second-order generalization of FCA can be built up in terms of the Chu construction.

[221]
I.P. Cabrera, P. Cordero, F. Garcia-Pardo, M. Ojeda-Aciego, and B. De Baets. On the construction of adjunctions between a fuzzy preposet and an unstructured set. Fuzzy Sets and Systems, 320:81-92, 2017. [ bib | DOI | .pdf ]
In this work, we focus on adjunctions, also called isotone Galois connections, in the framework of fuzzy preordered sets (hereafter, fuzzy preposets). Specifically, we present necessary and sufficient conditions so that, given a mapping f : A -> B from a fuzzy preposet A into an unstructured set B, it is possible to construct a suitable fuzzy preorder relation on B for which there exists a mapping g: B -> A such that the pair (f,g) constitutes an adjunction.

[220]
P. Julián, J. Medina, and M. Ojeda-Aciego. On reductants in the framework of multiadjoint logic programming. Fuzzy Sets and Systems, 317:27-43, 2017. [ bib | DOI | .pdf ]
Reductants are a special kind of fuzzy rules which constitute an essential theoretical tool for proving correctness properties. As it has been reported, when interpreted on a partially ordered structure, a multi-adjoint logic program has to include all its reductants in order to preserve the (approximate) completeness property. After a short survey of the different notions of reductant that have been developed for multi-adjoint logic programs, we introduce a new and more adequate, notion of reductant in the mult-adjoint framework. We study some of its properties and its relationships with other notions of reductants. In addition, we give an efficient algorithm for computing all the reductants associated with a multi-adjoint logic program.

[219]
I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Characterizing the existence of residual for a morphism between a fuzzy preposet and an unordered fuzzy structure. In Proc. of the Biennial Congress of the Royal Spanish Mathematical Society RSME'17, 2017. [ bib ]
[218]
J. Medina, M. Ojeda-Aciego, J. Pócs, and E. Ramírez-Poussa. On the Dedekind-MacNeille completion and formal concept analysis based on multilattices. Fuzzy Sets and Systems, 303:1-20, 2016. [ bib | DOI | .pdf ]
The Dedekind-MacNeille completion of a poset P can be seen as the least complete lattice containing P. In this work, we analyze some results concerning the use of this completion within the framework of Formal Concept Analysis in terms of the poset of concepts associated with a Galois connection between posets. Specifically, we show an interesting property of the Dedekind-MacNeille completion, in that the completion of the concept poset of a Galois connection between posets coincides with the concept lattice of the Galois connection extended to the corresponding completions. Moreover, we study the specific case when P has multilattice structure and state and prove the corresponding representation theorem.

[217]
M. Ojeda-Aciego and J. Outrata. Guest editorial: Concept lattices and their applications. Intl J of General Systems, 45(2):55-56, 2016. [ bib | DOI ]
[216]
M. Ojeda-Aciego, D. Ignatov, and A. Lepskiy, editors. Soft Computing Applications and Knowledge Discovery (SCAKD'16), volume 1687 of CEUR Proceedings, 2016. [ bib | http ]
[215]
J. Konecny and M. Ojeda-Aciego. On homogeneous L-bonds and heterogeneous L-bonds. Intl J of General Systems, 45(2):160-186, 2016. [ bib | DOI | .pdf ]
In this paper we deal with suitable generalizations of the notion of bond between contexts, as part of the research area of Formal Concept Analysis. We study different generalizations of the notion of bond within the L-fuzzy setting. Specifically, given a formal context there are three prototypical pairs of concept-forming operators, and this immediately leads to three possible versions of the notion of bond (so-called homogeneous bond wrt certain pair of concept-forming operators). The first results show a close correspondence between a homogeneous bond between two contexts and certain special types of mappings between the sets of extents (or intents) of the corresponding concept lattices. Later, we introduce the so-called heterogeneous bonds (considering simultaneously two types of concept-forming operators) and generalize the previous relationship to mappings between the sets of extents (or intents) of the corresponding concept lattices.

[214]
N. Madrid, J. Medina, M. Ojeda-Aciego, and I. Perfilieva. Toward the use of fuzzy relations in the definition of mathematical morphology operators. Journal of Fuzzy Set Valued Analysis, 2016(1):12 pages, 2016. [ bib | DOI ]
In this paper we present a definition of erosions and dilations in terms of fuzzy relations and adjoint triples. We firstly show that we can represent any algebraic erosion and dilation in such a terms and secondly, we present a set of approaches that can be covered by our definition of relational erosions and dilations.

[213]
A. Burrieza, E. Muñoz-Velasco, and M. Ojeda-Aciego. A hybrid approach to closeness in the framework of order of magnitude qualitative reasoning. Lect. Notes in Computer Science, 9648:721-729, 2016. [ bib | DOI ]
Qualitative reasoning deals with information expressed in terms of qualitative classes and relations among them, such as comparability, negligibility or closeness. In this paper, we focus on the notion of closeness using a hybrid approach which is based on logic, order-of-magnitude reasoning, and on the so-called proximity structures; these structures will be used to decide the elements that are close to each other. Some of the intuitions of this approach are explained on the basis of examples. Moreover, we show some capabilities of the logic with respect to expressivity in order to denote particular positions of the proximity intervals.

[212]
O. Krídlo and M. Ojeda-Aciego. On the n-ary generalization of dual bonds. In Proc. of the European Symposium on Computational Intelligence and Mathematics ESCIM'16, pages 55-59, 2016. [ bib | .pdf ]
We propose the generalization of the notion of bond between two formal contexts to the case of n formal contexts. The first properties of the n-ary bonds are given, together with a method for building n-ary bonds. This construction enables to formalize some inference rules within the research topic of building a sequent calculus for formal contexts.

[211]
M. Ojeda-Aciego. Bonds in a fuzzy environment. In Proc. of the European Symposium on Computational Intelligence and Mathematics ESCIM'16, page 30, 2016. Keynote talk. [ bib | .pdf ]
Formal Concept Analysis (FCA) has become a very active research topic, both theoretical and practical; its wide applicability justifies the need of a deeper knowledge of its underlying mechanisms, and one important way to obtain this extra knowledge turns out to be via generalization. Several fuzzy variants of generalized FCA have been introduced and developed both from the theoretical and the practical side. Most of the generalizations focus on including extra features (fuzzy, possibilistic, rough, etc.); however, not much have been published on the suitable general version of certain specific notions, such as the bonds between formal contexts. One of the motivations for introducing the notion of bond was to provide a tool for studying mappings between formal contexts, somehow mimicking the behavior of Galois connections between their corresponding concept lattices. In this talk we will deal with generalizations of the notion of bond in an L-fuzzy setting.

[210]
O. Krídlo and M. Ojeda-Aciego. Towards a sequent calculus for formal contexts. In Proc. of “What can FCA do for Artificial Intelligence?” FCA4AI, collocated with ECAI'16., 2016. [ bib | .pdf ]
This work focuses on the definition of a consequence relation between contexts with which we can decide whether certain contextual information is a logical consequence from a set of contexts considered as underlying hypotheses.

[209]
I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. On fuzzy relations, functional relations, and adjunctions. In Proc. of Foundations of Computational Intelligence, FOCI, 2016. [ bib | DOI | .pdf ]
[208]
I.P. Cabrera, P. Cordero, B. De Baets, F. García-Pardo, and M. Ojeda-Aciego. On the existence of right adjoints for surjective mappings between fuzzy structures. In Proc. of Concept Lattices and their Applications, CLA, 2016. [ bib | .pdf ]
We continue our study of the characterization of existence of adjunctions (isotone Galois connections) whose codomain is insufficiently structured. This paper focuses on the fuzzy case in which we have a fuzzy ordering rho_A on A and a surjective mapping f: ( A, approx_A) -> ( B, approx_B) compatible with respect to the fuzzy equivalences approx_A and approx_B. Specifically, the problem is to find a fuzzy ordering rho_B and a compatible mapping g: (B, approx_B) -> (A, approx_A) such that the pair (f,g) is a fuzzy adjunction.

[207]
I.P. Cabrera, P. Cordero, B. De Baets, F. García-Pardo, and M. Ojeda-Aciego. Fuzzy adjunction revisited. In Proc. of the Spanish Conference on Fuzzy Logic and Technology, ESTYLF, 2016. [ bib ]
[206]
I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. The natural embedding of fuzzy preposets and its residual mapping. In Proc. of Computational and Mathematical Methods in Science and Engineering, CMMSE, 2016. [ bib ]
[205]
F. García-Pardo, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Constructing right adjoints between fuzzy preordered sets. In Proc. of the Conference of the Spanish Association for Artificial Intelligence, CAEPIA, 2015. [ bib ]
In this work, we focus on the study of necessary and sufficient conditions in order to ensure the existence (under some constraints) of monotone Galois connections between fuzzy preordered sets.

[204]
A. Burrieza, E. Muñoz, and M. Ojeda-Aciego. Logic-based order of magnitude qualitative reasoning for closeness via proximity intervals: a first approach. In Proc. of the Conference of the Spanish Association for Artificial Intelligence, CAEPIA, 2015. [ bib ]
Qualitative reasoning is an area of AI which provides solutions to problems where the quantitative information either is not available or can not be used; in particular, order of magnitude qualitative reasoning assumes different qualitative classes and relations such as negligibility and closeness. In this paper, we focus mainly on the very important notion of closeness from the logical point of view, which has not received much attention in the literature. Our notion of closeness is based on the so-called proximity intervals, which will be used to decide the elements that are close to each other. Some of the intuitions of this definition are explained on the basis of examples. We introduce a multimodal logic for order of magnitude reasoning which includes the notions of closeness and negligibility, we provide an axiom system, which is sound and complete.

[203]
J. Medina, M. Ojeda-Aciego, and J. Pócs. Concepts and multilattices: the distributivity of the Dedekind-MacNeille completion. In Proc. of the Conference of the Spanish Association for Artificial Intelligence, CAEPIA, 2015. [ bib ]
The Dedekind-MacNeille completion of a poset P can be seen as the least complete lattice containing P . In this work, we analyze some results concerning the use of this completion within the framework of Formal Concept Analysis, notably the distributivity of the Dedekind- MacNeille completion and the construction of the poset of concepts as- sociated with a Galois connection between posets.

[202]
F. García-Pardo, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. On fuzzy preordered sets and monotone Galois connections. In IEEE Symposium on Foundations of Computational Intelligence, FOCI 2015, 2015. [ bib | .pdf ]
In this work, we focus on the study of necessary and sufficient conditions in order to ensure the existence (under some constraints) of monotone Galois connections between fuzzy preordered sets.

[201]
L. Antoni, I. P. Cabrera, S. Krajči, O. Krídlo, and M. Ojeda-Aciego. Using the Chu construction for generalizing formal concept analysis. In Proc. of Concept Lattices and their Applications, 2015. [ bib | .pdf ]
The goal of this paper is to show a connection between FCA generalisations and the Chu construction on the category ChuCors, the category of formal contexts and Chu correspondences. All needed categorical properties like categorical product, tensor product and its bifunctor properties are presented and proved. Finally, the second order generalisation of FCA is represented by a category built up in terms of the Chu construction.

[200]
P. Cordero, M. Enciso, A. Mora, M. Ojeda-Aciego, and C. Rossi. Knowledge discovery in social networks by using a logic-based treatment of implications. Knowledge-Based Systems, 87:16-25, 2015. [ bib | http ]
This work can be seen as a contribution to the area of social network analysis. By considering Formal Concept Analysis (FCA) as the underlying formalizing tool, we use logic-based techniques in order to offer novel solutions to identify user's influence in a social network. We propose the use of the Simplification Logic SLFD for attribute implications as the core of an automated method to build a structure containing the complete set of influences among users.

[199]
M. Ojeda-Aciego, J. Baixeries, and C. Sacarea, editors. Formal Concept Analysis and Applications, volume 1434 of CEUR Proceedings, 2015. [ bib | http ]
[198]
H. Bustince, N. Madrid, and M. Ojeda-Aciego. The notion of weak-contradiction: definition and measures. IEEE Transactions on Fuzzy Systems, 23(4):1057-1069, 2015. [ bib | http | .pdf ]
In this work we present a way to represent contradiction between fuzzy sets. This representation is given in terms of the notion of f-weak contradiction. Unlike other approaches, we do not define contradiction just by using one of the relations of f- weak-contradiction, but by considering the whole set of relations. This consideration avoids the need to fix an operator beforehand in order to take into account all the information between two fuzzy sets. As a result, we characterize the contradiction between fuzzy sets and define a family of measures of contradiction satisfying four interesting properties: symmetry, antitonicity, if the intersection is empty then the measure is one; and if there is an element in the intersection with degree of membership 1 then the measure is zero.

[197]
F. García-Pardo, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. On closure systems and adjunctions between fuzzy preordered sets. Lect. Notes in Computer Science, 9113:114-127, 2015. [ bib ]
The aim of this work is providing a characterization in terms of closure systems, for the construction, given a mapping f: A -> B from a fuzzy preordered set A into an unstructured set B, of a suitable fuzzy preordering on B for which there exists a mapping g: B -> A such that the pair (f,g) constitutes an adjunction (isotone Galois connection). This contribution continues our research line on the construction of adjunctions in which the theory of fuzzy closure systems is used in order to provide a more meaningful framework for the extension to the fuzzy case of previous results.

[196]
J. Baixeries, M. Ojeda-Aciego, and C. Sacarea, editors. Formal Concept Analysis, volume 9113 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 2015. [ bib | http ]
[195]
N. Madrid, M. Ojeda-Aciego, and I. Perfilieva. f-inclusion indexes between fuzzy sets. In Proc. of IFSA-EUSFLAT, 2015. [ bib | http ]
We introduce the notion of f-inclusion, which is used to describe different kinds of subsethood relations between fuzzy sets by means of monotonic functions f: [0,1] -> [0,1]. We show that these monotonic functions can be considered indexes of inclusion, since the greater the function considered, the more restrictive is the relationship. Finally, we propose a general index of inclusion by proving the existence of a representative f-inclusion for any two ordered pairs of fuzzy sets. In such a way, our approach is different to others in the literature in no taking a priori assumptions like residuated implications or t-norms.

[194]
E. Rodríguez, K. Bertet, P. Cordero, M. Enciso, A. Mora, and M. Ojeda-Aciego. From implicational systems to direct-optimal bases: a logic-based approach. Applied Mathematics and Information Sciences, 9(2L):1-13, 2015. [ bib | .pdf ]
Due to its solid mathematical foundations, Formal Concept Analysis (FCA) has become an emergent topic in the area of data analysis and knowledge discovering. Information is represented in a binary table defining a relation between a set of objects and a set of attributes?the formal context. The knowledge extracted from the formal context allows to identify useful patterns in data in different forms. One very useful knowledge representation in FCA are implications among attributes which are validated over the objects. The most outstanding feature of implications is that they can be managed by means of inference systems. Equivalent sets of implications can be obtained using different logic-based transformations. The aim of these transformations is to turn the original set of implications into an equivalent one fulfilling some desired properties. Among them, the directness and optimality are very popular targets because getting a direct-optimal basis ensures that the closure of a set of attributes may be computed with lower cost (time and resources). In this work, we introduce a new method to compute the direct-optimal basis which improves the existing ones. The new method reduces the input in a first stage and is guided by the idea of limiting the growth of the intermediate sets of implications as a way to improve the performance. We illustrate the good features of the new method with both a detailed example and by experimental evaluation.

[193]
I.P. Cabrera, P. Cordero, F. García, and M. Ojeda-Aciego. On the definition of fuzzy adjunction. In Proc. of XXIV CEDYA/XIV Congress on Applied Mathematics, pages 307-308, 2015. [ bib ]
[192]
I.P. Cabrera, P. Cordero, F. García, and M. Ojeda-Aciego. On the notion of fuzzy adjunctions between fuzzy orders. In Proc. of Computational Methods in Mathematics, Science, and Engineering (CMMSE 2015), pages 267-274, 2015. [ bib ]
[191]
O. Krídlo and M. Ojeda-Aciego. Linking L-Chu correspondences and completely lattice L-ordered sets. Annals of Mathematics and Artificial Intelligence, 72(1-2):91-113, 2014. [ bib | http | .pdf ]
Continuing our categorical study of L-fuzzy extensions of formal concept analysis, we provide a representation theorem for the category of L-Chu correspondences between L-formal contexts and prove that it is equivalent to the category of completely lattice L-ordered sets.

[190]
J. Konecny, J. Medina, and M. Ojeda-Aciego. Multi-adjoint concept lattices with heterogeneous conjunctors and hedges. Annals of Mathematics and Artificial Intelligence, 72(1-2):73-89, 2014. [ bib | http | .pdf ]
This paper is related, on the one hand, to the framework of multi-adjoint concept lattices with heterogeneous conjunctors and, on the other hand, to the use of intensifying hedges as truth-stressers. Specifically, we continue on the line of recent works by Belohlavek and Vychodil, which use intensifying hedges as a tool to reduce the size of a concept lattice. In this paper we use hedges as a reduction tool in the general framework of multi-adjoint concept lattices with heterogeneous conjunctors.

[189]
F. García-Pardo, I.P. Cabrera, P. Cordero, M. Ojeda-Aciego, and F.J. Rodríguez. On the definition of suitable orderings to generate adjunctions over an unstructured codomain. Information Sciences, 286:173-187, 2014. [ bib | http | .pdf ]

[188]
P. Julián, J. Medina, and M. Ojeda-Aciego. Revisiting reductants in the multi-adjoint logic programming framework. Lect. Notes in Artificial Intelligence, 8761:694-702, 2014. [ bib | http | .pdf ]

[187]
I.P. Cabrera, M. Ojeda-Aciego, and Jozef Pócs. Ordering objects via attribute preferences. In Proc. of Concept Lattices and their Applications, pages 157-168, 2014. [ bib | .pdf ]
We apply recent results on the construction of suitable orderings for the existence of right adjoint to the analysis of the following problem: given a preference ordering on the set of attributes of a given context, we seek an induced preference among the objects which is compatible with the information provided by the context.

[186]
N. Madrid, J. Medina, J.C. Moreno, and M. Ojeda-Aciego. New links between mathematical morphology and fuzzy property-oriented concept lattices. In IEEE Intl Conf on Fuzzy Systems (FUZZ-IEEE'14), pages 600-603, 2014. [ bib | http | .pdf ]
The theory of fuzzy property-oriented concept lattices is a formal tool for modeling and processing incomplete knowledge in information systems. This paper relates this research topic to that of mathematical morphology, a theory whose scope is to process and analyze images and signals. Consequently, the theory developed in the concept lattice framework can be used in these particular settings.

[185]
P. Eklund, M.A. Galán, J. Kortelainen, and M. Ojeda-Aciego. Monadic formal concept analysis. Lect. Notes in Computer Science, 8536:201-210, 2014. [ bib ]
Formal Concept Analysis (FCA) as inherently relational can be formalized and generalized by using categorical constructions. This provides a categorical view of the relation between 'object' and 'attributes', which can be further extended to a more generalized view on relations as morphisms in Kleisli categories of suitable monads. Structure of sets of 'objects' and 'attributes' can be provided e.g. by term monads over particular signatures, and specific signatures drawn from and developed within social and health care can be used to illuminate the use of the categorical approach.

[184]
F. García-Pardo, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. On adjunctions between fuzzy preordered sets: Necessary conditions. Lect. Notes in Computer Science, 8536:211-221, 2014. [ bib | .pdf ]
There exists a direct relation between fuzzy rough sets and fuzzy preorders. On the other hand, it is well known the existing parallelism between Formal Concept Analysis and Rough Set Theory. In both cases, Galois connections play a central role. In this work, we focus on adjunctions (also named isotone Galois connections) between fuzzy preordered sets; specifically, we study necessary conditions that have to be fulfilled in order such an adjunction to exist.

[183]
F. García-Pardo, I.P. Cabrera, P. Cordero, M. Ojeda-Aciego, and F.J. Rodríguez. On the existence of isotone Galois connections between preorders. Lect. Notes in Computer Science, 8478:67-79, 2014. [ bib | .pdf ]
Given a mapping from a preordered set A into an unstructured set B, we study the problem of defining a suitable preordering relation on B such that there exists a mapping g from B to A such that the pair (f, g) forms an adjunction between preordered sets.

[182]
F. García-Pardo, I.P. Cabrera, P. Cordero, M. Ojeda-Aciego, and F.J. Rodríguez. Generating isotone Galois connections on an unstructured codomain. Communications in Computer and Information Science, 444:91-99, 2014. [ bib | .pdf ]
Given a mapping f from a partially ordered set A into an unstructured set B, we study the problem of defining a suitable partial ordering relation on B such that there exists a mapping g from B to A such that the pair of mappings (f, g) forms an isotone Galois connection between partially ordered sets.

[181]
A. Burrieza, E. Muñoz, and M. Ojeda-Aciego. A logic framework for reasoning with movement based on fuzzy qualitative representation. Fuzzy Sets and Systems, 242:114-131, 2014. [ bib | http | .pdf ]
We present a logic approach to reason with moving objects under fuzzy qualitative representation. This way, we can deal both with qualitative and quantitative information, and consequently, to obtain more accurate results. The proposed logic system is introduced as an extension of Propositional Dynamic Logic: this choice, on the one hand, simplifies the theoretical study concerning soundness, completeness and decidability; on the other hand, provides the possibility of constructing complex relations from simpler ones and the use of a language very close to programming languages.

[180]
J.C. Díaz, J. Medina, and M. Ojeda-Aciego. On basic conditions to generate multi-adjoint concept lattices via Galois connections. Intl Journal of General Systems, 43(2):149-161, 2014. [ bib | http | .pdf ]
This paper introduces sufficient and necessary conditions with respect to the fuzzy operators considered in a multi-adjoint frame under which the standard combinations of multi-adjoint sufficiency, possibility and necessity operators form (antitone or isotone) Galois connections. The underlying idea is to study the minimal algebraic requirements so that the concept-forming operators (defined using the same syntactical form than the extension and intension operators of multi-adjoint concept lattices) form a Galois connection. As a consequence, given a relational database, we have much more possibilities to construct concept lattices associated with it, so that we can choose the specific version which better suits the situation.

[179]
F. García-Pardo, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. On the construction of fuzzy Galois connections. In XVII Spanish Conference on Fuzzy Logic and Technology, pages 99-102, 2014. [ bib ]
Given a mapping from a fuzzy poset (A, ?) to any set B, we introduce conditions which allow for defining a fuzzy ordering on B and a mapping from B to A such that the pair (f ,g) forms a fuzzy Galois connection

[178]
I.P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. On residuation in multilattices: filters, congruences, and homomorphisms. Fuzzy Sets and Systems, 234:1-21, 2014. [ bib | http | .pdf ]
Continuing with our general study of algebraic hyperstructures, we focus on the residuated operation in the framework of multilattices. Firstly, we recall the existing relation between filters, homomorphisms and congruences in the framework of multilattices; then, introduce the notion of residuated multilattice and further study the notion of filter, which has to be suitably modified so that the results in the first section are conveniently preserved also in the residuated case.

[177]
P. Cordero, M. Enciso, A. Mora, and M. Ojeda-Aciego. Computing left-minimal direct basis of implications. In Proc. of Concept Lattices and Applications, CLA 2013, pages 293-298, 2013. [ bib | .pdf ]
The most popular basis in Formal Concept Analysis is the Duquenne-Guigues basis, which ensure minimality in the number of dependencies and it is built with pseudo-intents, and some method to calculate these basis from an arbitrary set of implications have been introduced. We propose in this paper, an automated method to calculate a left-minimal direct basis from the set of all implications built between a closed set and its corresponding minimal generators. The new basis also has the minimal property demanded in the Duquenne-Guigues basis. It is minimal in the cardinal of the set of implications, and minimal in the size of the left-hand side of the implications.

[176]
O. Krídlo and M. Ojeda-Aciego. CRL-Chu correspondences. In Proc. of Concept Lattices and Applications, CLA 2013, pages 105-116, 2013. [ bib | .pdf ]
We continue our study of the general notion of L-Chu correspondence by introducing the category CRL-ChuCors incorporating residuation to the underlying complete lattice L, specifically, on the basis of a residuation-preserving isotone Galois connection ?. Then, the L-bonds are generalized within this same framework, and its structure is related to that of the extent of a suitably defined ?-direct product.

[175]
J. Konecny and M. Ojeda-Aciego. Isotone L-bonds. In Proc. of Concept Lattices and Applications, CLA 2013, pages 153-162, 2013. [ bib | .pdf ]
L-bonds represent relationships between formal contexts. We study properties of these intercontextual structures w.r.t. isotone concept- forming operators in fuzzy setting. We also focus on the direct product of two formal fuzzy contexts and show conditions under which a bond can be obtained as an intent of the product. In addition, we show that the previously studied properties of their antitone counterparts can be easily derived from the present results.

[174]
M. Ojeda-Aciego and J. Outrata, editors. Concept Lattices and Their Applications, volume 1062 of CEUR Proceedings, 2013. [ bib | http ]
[173]
H. Bustince, N. Madrid, and M. Ojeda-Aciego. A measure of contradiction based on the notion of n-weak-contradiction. In IEEE Intl Conf on Fuzzy Systems (FUZZ-IEEE'13), pages 1-6, 2013. [ bib | http | .pdf ]
In this work we elaborate on the notion of contradiction between fuzzy sets introduced by Trillas et al in a fuzzy logic context. Our approach is parametric in that the operator used to define contradiction is rather a variable than a constant introduced prior to the analysis of contradiction. We give several motivations to consider weaker operators than the usual involutive negations, and obtain some preliminary results which validate this proposal.

[172]
J.C. Díaz, J. Medina, and M. Ojeda-Aciego. On minimal requirements to obtain fuzzy concept-forming operators. In Intl Conference on Fuzzy Logic and Technology (EUSFLAT'13), pages 796-801, 2013. [ bib | http ]
In this work, we introduce sufficient and necessary conditions for a pair of fuzzy conjunctor and implication considered in a multi-adjoint frame under which the usual combinations of multi-adjoint sufficiency, possibility and necessity operators form either antitone or isotone Galois connections.

[171]
P. Cordero, M. Enciso, A. Mora, and M. Ojeda-Aciego. Bases via minimal generators. In IJCAI workshop on FCA for AI, pages 33-36, 2013. [ bib | .pdf ]
The concept lattice corresponding to a context may be alternatively specified by means of attribute implications. One outstanding problem in formal concept analysis and other areas is the study of the equivalences between a given set of implications and its corresponding basis (notice that there exists a wide range of approaches to basis in the literature). In this work we introduce a method to provide a Duquenne-Guigues basis corresponding to the minimal generators and their closed sets from a context

[170]
P. Cordero, M. Enciso, A. Mora, and M. Ojeda-Aciego. A method to extract precise implication from contexts. In Computational Methods in Mathematics, Science, and Engineering, 2013. [ bib | .pdf ]

[169]
F. García-Pardo, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego. On Galois connections and soft computing. Lect. Notes in Computer Science, 7903:224-235, 2013. [ bib | .pdf ]
After recalling the different interpretations usually assigned to the term Galois connection, both in the crisp and in the fuzzy case, we survey on several of their applications in Computer Science and, specifically, in Soft Computing.

[168]
P. Julián, J. Medina, P.J. Morcillo, G. Moreno, and M. Ojeda-Aciego. An unfolding-based preprocess for reinforcing thresholds in fuzzy tabulation. Lect. Notes in Computer Science, 7902:647-655, 2013. [ bib | .pdf ]
We have recently proposed a technique for generating thresholds (filters) useful for avoiding useless computations when executing fuzzy logic programs in a tabulated way. The method was conceived as a static preprocess practicable on program rules before being executed with our fuzzy thresholded tabulation principle, thus increasing the opportunities of prematurely disregarding those computation steps which are redundant (tabulation) or directly lead to non-significant solutions (thresholding). In this paper we reinforce the power of such static preprocess-which obviously does not require the consumption of extra computational resources at execution time-by re-formulating it in terms of the fuzzy unfolding technique initially designed in our group for transforming and optimizing fuzzy logic programs.

[167]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. Concept-forming operators on multilattices. In Intl Conf on Formal Concept Analysis, Lecture Notes in Artificial Intelligence 7880, pages 203-215, 2013. [ bib | .pdf ]
Adjoint pairs or adjoint triples defined on lattices have proven to be a useful tool when working in fuzzy formal concept analysis. This paper shows that adjoint pairs and triples can play as well an important role within the framework of multilattices, especially in order to form the Galois connections needed to build concept multilattices.

[166]
N. Madrid and M. Ojeda-Aciego. On the measure of incoherent information in extended multi-adjoint logic programs. In IEEE Symposium on Foundations of Computational Intelligence, FOCI 2013, pages 30-37, 2013. [ bib | .pdf ]
In this paper we continue analyzing the introduction of negation into the framework of residuated logic programming; specifically, we focus on extended programs, that is we consider programs with strong negation. The classical approach to extended logic programs consists in considering negated literals as new, independent, ones and, then apply the usual monotonic approach (based on the fix-point semantics and the TP operator); if the least fix-point so obtained is inconsistent, then the approach fails and no meaning is attached to the program. This paper introduces several approaches to measure consistency (under the term coherence) into a multi-adjoint setting.

[165]
J. Medina and M. Ojeda-Aciego. Dual multi-adjoint concept lattices. Information Sciences, 225:47-54, 2013. [ bib | http | .pdf ]
Several papers relate different alternative approaches to classical concept lattices: such as property-oriented and object-oriented concept lattices and the dual concept lattices. Whereas the usual approach to the latter is via a negation operator, this paper presents a fuzzy generalization of the dual concept lattice, the dual multi-adjoint concept lattice, in which the philosophy of the multi-adjoint paradigm is applied and no negation on the lattices is needed.

[164]
P. Cordero, M. Enciso, A. Mora, and M. Ojeda-Aciego. Computing minimal generators from implications: a logic-guided approach. In Proc. of Concept Lattices and Applications, CLA 2012, pages 187-198, 2012. [ bib | .pdf ]
Sets of attribute implications may have a certain degree of redundancy and the notion of basis appears as a way to characterize the implication set with less redundancy. The most widely accepted is the Duquenne-Guigues basis, strongly based on the notion of pseudo-intents. In this work we propose the minimal generators as an element to remove redundancy in the basis.

The main problem is to enumerate all the minimal generators from a set of implications. We introduce a method to compute all the minimal generators which is based on the Simplification Rule for implications. The simplification paradigm allows us to remove redundancy in the implications by deleting attributes inside the implication without removing the whole implication itself. In this work, the application of the Simplification Rule to the set of implications guides the search of the minimal generators in a logic-based style, providing a deterministic approach.

[163]
O. Krídlo and M. Ojeda-Aciego. Linking L-chu correspondences and completely lattice L-valued sets. In Proc. of Concept Lattices and Applications, CLA 2012, pages 233-244, 2012. [ bib | .pdf ]
Continuing our categorical study of L-fuzzy extensions of formal concept analysis, we provide a representation theorem for the category of L-Chu correspondences between L-formal contexts and prove that it is equivalent to the category of completely lattice L-ordered sets.

[162]
J. Konecny, J. Medina, and M. Ojeda-Aciego. Intensifying hedges and the size of multi-adjoint concept lattices with heterogeneous conjunctors. In Proc. of Concept Lattices and Applications, CLA 2012, pages 245-256, 2012. [ bib | .pdf ]
In this work we focus on the use of intensifying hedges as a tool to reduce the size of the recently introduced multi-adjoint concept lattices with heterogeneous conjunctors.

[161]
N. Madrid and M. Ojeda-Aciego. On least coherence-preserving negations. In 31st Meeting of the North-American Fuzzy Information Processing Society, NAFIPS'12, 2012. [ bib | http ]
We focus on the notion of coherent L-interpretations with respect to a negation operator, as a convenient generalization to a fuzzy or multiple-valued environment of the classical notion of consistent interpretation. We show that, given an L-interpretation I, the set of negation operators n satisfying that I is coherent wrt n has a structure of complete lattice; so there exists the greatest and the least negation operators satisfying such property; moreover, the expression of the least negation operator n satisfying that I is coherent wrt n is presented. Finally, for the case in which the underlying set of truth-values is the real unit interval [0,1], we describe a method to achieve a practical expression for the least coherence-preserving negation.

[160]
I.P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. Filters and deductive systems on residuated multilattices. In 10th Int FLINS Conference on Uncertainty Modeling in Knowledge Engineering and Decision Making, 2012. [ bib ]
We continue the study of the residuated operations in the framework of hyperstructures. We focus on the case of a multilattice as underlying algebraic structure and introduce the notions of filter and deductive system. They differ from the analogous concepts in a pocrim due to the connection to congruence relations. Finally, we prove that the set of filters of a residuated multilattice is a complete lattice.

[159]
J. Medina and M. Ojeda-Aciego. On multi-adjoint concept lattices based on heterogeneous conjunctors. Fuzzy Sets and Systems, 208:95-110, 2012. [ bib | http | .pdf ]
Sets of attributes and objects in fuzzy formal concept analysis are usually different and, hence, it might not make sense to evaluate them on the same carrier. In this context, the operators used to obtain the concept lattice could be defined by associating different lattices to attributes and objects; several reasons exist for which we need to evaluate the sets of attributes and objects in the same carrier. Following this direction, we introduce a new definition of a concept lattice, where objects and attributes are evaluated on the same lattice L, although operators evaluating objects and attributes in different carriers are used. Moreover, we study the relationship between this new concept lattice and the alternative one which can be obtained directly by using different carriers for the sets of attributes and objects.

[158]
N. Madrid and M. Ojeda-Aciego. On the existence and unicity of stable models in normal residuated logic programs. Intl J of Computer Mathematics, 89(3):310-324, 2012. [ bib | http | .pdf ]
We introduce a sufficient condition which guarantees the existence of stable models for a normal residuated logic program interpreted on the truth-space [0, 1]n. Specifically, the continuity of the connectives involved in the program ensures the existence of stable models. Then, we study conditions which guarantee the uniqueness of stable models in the particular case of the product t-norm, its residuated implication, and the standard negation.

[157]
I.P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. Finitary coalgebraic multisemilattices and multilattices. Applied Mathematics and Computation, 219(1):31-44, 2012. [ bib | http | .pdf ]
In this paper we continue the coalgebraization of the structure of multilattice. Specifically, we introduce a coalgebraic characterization of the notion of finitary multi(semi)lattice, a generalization of that of semilattice which arises naturally in several areas of computer science and provides the possibility of handling non-determinism.

[156]
O. Krídlo, S. Krajči, and M. Ojeda-Aciego. The category of L-Chu correspondences and the structure of L-bonds. Fundamenta Informaticae, 115(4):297-325, 2012. [ bib | http | .pdf ]
An L-fuzzy generalization of the so-called Chu correspondences between formal contexts forms a category called L-ChuCors. In this work we show that this category naturally embeds ChuCors, and prove that it is *-autonomous. We also focus on the direct product of two L-fuzzy contexts, which is defined with the help of a binary operation, essentially a disjunction, on a lattice of truth-values L.

[155]
I.P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. Residuated operations in hyperstructures: residuated multilattices. In Computational Methods in Mathematics, Science, and Engineering, 2011. [ bib | .pdf ]
We initiate the exploration of the residuated operations in the framework of hyperstructures. We focus on the case of a multilattice as underlying algebraic structure, introduce the notion of residuated multilattice and study some of its properties, among which we have shown that the idempotency of the monoidal operation characterises the subclass of Heyting algebras.

[154]
A. Burrieza, E. Muñoz, and M. Ojeda-Aciego. PDL for qualitative reasoning about moving objects: first steps. In Proc. Intl Qualitative Reasoning Workshop 2011, 2011. Accepted. [ bib | .pdf ]
[153]
C.V. Damásio, N. Madrid, and M. Ojeda-Aciego. On the notions of residuated-based coherence and bilattice-based consistence. Lecture Notes in Computer Science, 6857:115-122, 2011. [ bib | .pdf ]
Different notions of coherence and consistence have been proposed in the literature on fuzzy systems. In this work we focus on the relationship between some of the approaches developed, on the one hand, based of residuated lattices and, on the other hand, based on the theory of bilattices.

[152]
I. P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Non-deterministic algebraic structures for soft computing. Lecture Notes in Computer Science, 6692:437-444, 2011. [ bib | .pdf ]
The need of considering non-determinism in theoretical computer science has been claimed by several authors in the literature. The notion of non-deterministic automata as a formal model of computation is widely used, but the specific study of non-determinism is useful, for instance, for natural language processing, in describing interactive systems, for characterizing the flexibility allowed in the design of a circuit or a network, etc. The most suitable structures for constituting the foundation of this theoretical model of computation are non-deterministic algebras. The interest on these generalized algebras has been growing in recent years, both from a crisp and a fuzzy standpoint. This paper presents a survey of these structures in order to foster its applicability for the development of new soft computing techniques.

[151]
P. Julián, J. Medina, G. Moreno, and M. Ojeda-Aciego. A static preprocess for improving fuzzy thresholded tabulation. Lecture Notes in Computer Science, 6692:429-436, 2011. [ bib | .pdf ]
[150]
O. Krídlo, S. Krajči, and M. Ojeda-Aciego. Functorial connection between L-ChuCors and a category of supremum preserving mappings. In Proc. of Intl Conf on Formal Concept Analysis, pages 39-52, 2011. [ bib | .pdf ]
The category of L-Chu correspondences between formal L-fuzzy contexts provides a categorical view on Formal Context Analysis. In this paper some interesting and useful properties are shown. The main aim of this paper is to introduce a functor between L-ChuCors and a category of supremum preserving mappings between completely L-ordered sets.

[149]
N. Madrid and M. Ojeda-Aciego. Measuring inconsistency in fuzzy answer set semantics. IEEE Transactions on Fuzzy Systems, 19(4):605-622, 2011. [ bib | http | .pdf ]
Recent approaches have shown that the measurement of the amount of inconsistent information contained in a logic theory can be useful to infer positive information.

This paper deals with the definition of measures of inconsistency in the residuated logic programming paradigm under the fuzzy answer set semantics. This fuzzy framework provides a soft mechanism of controlling the amount of information inferred and thus, controlling the inconsistencies by modifying slightly the truth-values of some rules.

[148]
N. Madrid and M. Ojeda-Aciego. On the use of fuzzy stable models for inconsistent classical logic programs. In IEEE Symposium on Foundations of Computational Intelligence, FOCI 2011, pages 115-121, 2011. [ bib | .pdf ]
We introduce a sufficient condition which guarantees the existence of stable models for a normal residuated logic program interpreted on the truth-space [0,1]n. Specifically, the continuity of the connectives involved in the program ensures the existence of stable models. Then, we focus on the assignment of a fuzzy stable model semantics to inconsistent classical logic programs on the basis of the separation of the notion of inconsistence and uncertainty.

[147]
O. Krídlo and M. Ojeda-Aciego. On L-fuzzy Chu correspondences. Intl J of Computer Mathematics, 88(9):1808-1818, 2011. [ bib | http | .pdf ]
In this paper, we focus on the framework of Chu correspondences introduced by Mori for classical formal concept analysis, and we propose a suitable extension of the framework in a more general and flexible environment based on L-fuzzy sets, and define the notions of L-Chu correspondence and of L-bond. After introducing the generalized framework, the sets of L-Chu correspondences and of L-bonds are proved to have the structure of complete lattice and, furthermore, there exists a natural anti-isomorphism between them.

[146]
A. Burrieza, E. Muñoz, and M. Ojeda-Aciego. A PDL approach for qualitative velocity. Intl J of Uncertainty, Fuzziness, and Knowledge-based Systems, 19(1):11-26, 2011. [ bib | http | .pdf ]
We introduce the syntax, semantics, and an axiom system for a PDL-based extension of the logic for order of magnitude qualitative reasoning, developed in order to deal with the concept of qualitative velocity, which together with qualitative distance and orientation, are important notions in order to represent spatial reasoning for moving objects, such as robots. The main advantages of using a PDL-based approach are, on the one hand, all the well-known advantages of using logic in AI, and, on the other hand, the possibility of constructing complex relations from simpler ones, the flexibility for using different levels of granularity, its possible extension by adding other spatial components, and the use of a language close to programming languages.

[145]
I.P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. A coalgebraic approach to non-determinism: applications to multilattices. Information Sciences, 180(22):4323-4335, 2010. [ bib | http | .pdf ]
Multilattices are a suitable generalization of lattices which enables to accommodate the formalization of non-deterministic computation; specifically, the algebraic characterization for multilattices provides a formal framework to develop tools in several fields of computer science. On the other hand, the usefulness of coalgebra theory has been increasing in the recent years, and its importance is undeniable. In this paper, somehow mimicking the use of universal algebra, we define a new kind of coalgebras (the ND-coalgebras) that allows to formalize non-determinism, and show that several concepts, widely used in computer science are, indeed, ND-coalgebras. Within this formal context, we study a minimal set of properties which provides a coalgebraic definition of multilattices.

[144]
O. Krídlo, S. Krajči, and M. Ojeda-Aciego. L-bonds vs extents of direct products of two L-fuzzy contexts. In Proc. of Concept Lattices and Applications, CLA 2010, pages 70-79, 2010. [ bib | .pdf ]
We focus on the direct product of two L-fuzzy contexts, which are defined with the help of a binary operation on a lattice of truth-values L. This operation, essentially a disjunction, is defined as klk->l, for k,linL where negation is interpreted as ¬l=l->0. We provide some results which extend previous work by Krötzsch, Hitzler and Zhang.

[143]
J. Medina and M. Ojeda-Aciego. Towards attribute reduction in multi-adjoint concept lattices. In Proc. of Concept Lattices and Applications, CLA 2010, pages 92-103, 2010. [ bib | .pdf ]
In Formal Concept Analysis, attribute reduction is a important step in order to reduce the complexity of the computation of the concept lattice. This reduction is more complex in fuzzy environments. In this paper, we will present a first approximation to reduce the set of attributes in the multi-adjoint concept lattice. The solution found is based on the development of specific results which allow us to reduce the number of attributes in the classical case, by detecting some relatively necessary and absolutely unnecessary attributes and, then, use linguistic labels in order to obtain a method to reduce the number of attributes in a multi-adjoint context, working up to some level of tolerance, and preserving the original lattice structure of the set of concepts.

[142]
O. Krídlo, S. Krajči, and M. Ojeda-Aciego. An embedding of ChuCors in L-ChuCors. In Computational Methods in Mathematics, Science, and Engineering, pages 583-588, 2010. [ bib | .pdf ]
An L-fuzzy generalization of the so-called Chu correspondences between formal contexts forms a category called L-ChuCors. In this work we show that this category naturally embeds ChuCors.

[141]
N. Madrid and M. Ojeda-Aciego. On the existence of stable models in normal residuated logic programs. In Computational Methods in Mathematics, Science, and Engineering, pages 598-604, 2010. [ bib | .pdf ]
We introduce a sufficient condition which guarantees the existence of stable models for a normal residuated logic program interpreted on the truth-space [0,1]n. Specifically, the continuity of the connectives involved in the program ensures the existence of stable models.

[140]
J. Medina and M. Ojeda-Aciego. On multi-adjoint concept lattices based on heterogeneous conjunctors. In Computational Methods in Mathematics, Science, and Engineering, pages 633-641, 2010. [ bib | .pdf ]
In formal concept analysis, the sets of attributes and objects are usually different, with different meaning and, hence, it might not make sense to evaluate them on the same carrier. In this context, the operators used to obtain the concept lattice could be defined by considering different lattices associated to attributes and objects. Anyway there exist several reasons for which we need to evaluate the set of attributes and objects in the same carrier. In this direction, we present in this paper a new concept lattice, where the objects and attributes are evaluated on the same lattice L, although operators which evaluate objects and attributes in different carriers are used. Moreover, we have studied the relationship between the new concept lattice and the other one obtained directly considered different carriers to both set of attributes and objects.

[139]
I.P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. Coalgebras and non-determinism: an application to multilattices. In Proc. of Physics and Computation, 2010. [ bib ]
Multilattices are a suitable generalization of lattices which enables to accommodate the formalization of non-deterministic computation; specifically, the algebraic characterization for multilattices provides a formal framework to develop tools in several fields of computer science. On the other hand, the usefulness of coalgebra theory has been increasing in the recent years, and its importance is undeniable. In this work, we define a new kind of coalgebras (the ND-coalgebras) that allows to formalize non-determinism, and show that several concepts, widely used in computer science are, indeed, ND-coalgebras. Within this formal context, we study a minimal set of properties which provides a coalgebraic definition of multilattices.

[138]
P. Julián, J. Medina, G. Moreno, and M. Ojeda-Aciego. Efficient thresholded tabulation for fuzzy query answering. In Proc of PROLE'10, 2010. (Short note). [ bib ]
Fuzzy logic programming represents a flexible and powerful declarative paradigm amalgamating fuzzy logic and logic programming, for which there exists different promising approaches described in the literature. In this work we propose an improved fuzzy query answering procedure for the so-called multi-adjoint logic programming approach, which avoids the re-evaluation of goals and the generation of useless computations thanks to the combined use of tabulation with thresholding techniques. The general idea is that, when trying to perform a computation step by using a given program rule R, we firstly analyze if such step might contribute to reach further significant solutions (non-tabulated yet). When it is the case, it is possible to avoid useless computation steps via rule R by using thresholds and filters based on the truth degree of R, as well as a safe, accurate and dynamic estimation of the maximum truth degree associated to its body.

[137]
N. Madrid and M. Ojeda-Aciego. Measuring instability in normal residuated logic programs: adding information. In IEEE Intl Conf on Fuzzy Systems (FUZZ-IEEE'10), pages 2244-2250, 2010. [ bib | http | .pdf ]
Inconsistency in the framework of general residuated logic programs can be, somehow, decomposed in two notions: incoherence and instability. In this work, we focus on the measure of instability of normal residuated programs. Some measures were already provided and initial results obtained in terms of the amount of information that have to be discarded in order to recover stability; in this paper, our interest is focused precisely on the case in which stability can be recovered by adding information to our program.

[136]
N. Madrid and M. Ojeda-Aciego. Measuring instability in normal residuated logic programs: discarding information. Communications in Computer and Information Science, 80:128-137, 2010. [ bib | http | .pdf ]
Inconsistency in the framework of general residuated logic programs can be, somehow, decomposed in two notions: incoherence and instability. In this work, we focus on the measure of instability of normal residuated programs. Some measures are provided and initial results are obtained in terms of the amount of information that have to be discarded in order to recover stability.

[135]
I.P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. On fuzzy homomorphisms between hyperrings. In XV Spanish Conference on Fuzzy Logic and Technology, pages 175-180, 2010. [ bib | .pdf ]
We focus on the study of the structure of hyperrings; in this paper, we recall the basics of crisp homomorphisms between hyperstructures, particularly, between hyperrings and, then, the notion of fuzzy homomorphism between hyperrings is established and its main properties are analysed.

[134]
N. Madrid and M. Ojeda-Aciego. On the notion of coherence in fuzzy answer set semantics. In XV Spanish Conference on Fuzzy Logic and Technology, pages 157-162, 2010. [ bib | .pdf ]
The notion of coherence, introduced in the context of fuzzy answer set programming (FASP), provides a metalogic condition on the obtained models in FASP. In this work, we relate it with the concept of N-contradiction which is used in the definition of antonyms.

[133]
J. Medina and M. Ojeda-Aciego. Multi-adjoint t-concept lattices. Information Sciences, 180(5):712-725, 2010. [ bib | http | .pdf ]
The t-concept lattice is introduced as a set of triples associated to graded tabular information interpreted in a non-commutative fuzzy logic. Following the general techniques of formal concept analysis, and based on the works by Georgescu and Popescu, given a non-commutative conjunctor it is possible to provide generalizations of the mappings for the intension and the extension in two different ways, and this generates a pair of concept lattices. In this paper, we show that the information common to both concept lattices can be seen as a sublattice of the Cartesian product of both concept lattices. The multi-adjoint framework can be applied to this general t-concept lattice, and its usefulness is illustrated by a working example.

[132]
B. Bouchon-Meunier, L. Magdalena, M. Ojeda-Aciego, J.L. Verdegay, and R.R. Yager, editors. Foundations of reasoning under uncertainty, volume 249 of Studies in fuzziness and soft computing. Springer-Verlag, 2010. [ bib | http ]
Uncertainty exists almost everywhere, except in the most idealized situations; it is not only an inevitable and ubiquitous phenomenon, but is also a fundamental scientific principle. Furthermore, uncertainty is an attribute of information and, usually, decision-relevant information is uncertain and/or imprecise, therefore the abilities to handle uncertain information and to reason from incomplete knowledge are crucial features of intelligent behaviour in complex and dynamic environments. By carefully exploiting our tolerance for imprecision and approximation we can often achieve tractability, robustness, and better descriptions of reality than traditional deductive methods would allow us to obtain. In conclusion, as we move further into the age of machine intelligence, the problem of reasoning under uncertainty, in other words, drawing conclusions from partial knowledge, has become a major research theme.

Not surprisingly, the rigorous treatment of uncertainty requires sophisticated machinery, and the present volume is conceived as a contribution to a better understanding of the foundations of information processing and decision-making in an environment of uncertainty, imprecision and partiality of truth.

This volume draws on papers presented at the 2008 Conference on Information Processing and Management of Uncertainty (IPMU) which was held in Málaga, Spain, organized by the University of Málaga, and brought together some of the world's leading experts in uncertainty handling.

Since its first edition, held in 1986, the focus of IPMU conferences has been on the development of foundations and technology needed for the construction of intelligent systems. Over the years, IPMU has grown steadily in visibility and importance, and has evolved into a leading conference in its field, embracing a wide-variety of methodologies for dealing with uncertainty and imprecision, and this explains the unusually wide variety of concepts, methods and techniques which are discussed in the book. The growth in importance of IPMU reflects the fact that as we move further into the age of machine intelligence and mechanized decision-making, the issue of how to deal with uncertain information becomes an issue of paramount concern.

The book starts with a revisited approach for possibilistic fuzzy regression methods proposed by Bisserier et al., in which the identification problem is reformulated according to a new criterion that assesses the model fuzziness independently of the collected data. Later, Bonissone et al. propose the fundamentals to design and construct a “forest” of randomly generated fuzzy decision trees in an approach which combines the robustness of multi-classifiers, the construction efficiency of decision trees, the power of the randomness to increase the diversity of the trees in the forest, and the flexibility of fuzzy logic and the fuzzy sets for data managing. The third contribution, by Delgado et al., is related to the well-known framework of mining association rules for extracting useful knowledge from databases; they introduce so-called double rules as a new type of rules which in conjunction with exception rules will describe in more detail the relationship between two sets of items. Next, Dubois discusses ignorance and contradiction, and argues that they cannot be viewed either as additional truth-values or processed in a truth-functional manner, and that doing it leads to weak or debatable uncertainty handling approaches.

The volume continues with Grzegorzewski's work, which introduces new algorithms for calculating the proper approximations by trapezoidal fuzzy numbers which preserves the expected interval. Next, Jenhani et al. investigate the problem of measuring the similarity degree between two normalized possibility distributions encoding preferences or uncertain knowledge. Later, Julián et al. propose an improved fuzzy query answering procedure for multi-adjoint logic programming which avoids the re-evaluation of goals and the generation of useless computations thanks to the combined use of tabulation with thresholding techniques. Then, Kacprzyk and Wilbik, focus on an extension of linguistic summarization of time series; ; in addition to the basic criterion of a degree of truth (validity), they also use a degree of imprecision, specificity, fuzziness and focus as an additional criteria.

In the final part of the volume, Kalina et al. discuss the possibility of applying the modified level-dependent Choquet integral to a monopersonal multicriterial decision-making problem; they propose an algorithm which produces an outranking of objects taking into account an interaction between criteria. Next, Llamazares and Marques Pereira consider mixture operators to aggregate individual preferences and characterize those that allow to extend some majorities rules, such as simple, Pareto and absolute special majorities, to the field of gradual preferences. Later, Mercier et al. concentrate on the links between the different operations that can be used in the theory of belief functions to correct the information provided by a source, given meta-knowledge about that source. Then, Miranda compares the different notions of conditional coherence within the behavioural theory of imprecise probabilities when all the referential spaces are finite. Finally, Soubaras focuses on evidential Markov chains as a suitable generalization of classical Markov chains to the Dempster-Shafer theory, replacing the involved states by sets of states.

Last, but not least, we would like to thank the following institutions for their help with the organization of the 12th IPMU Conference: Ministerio de Educación y Ciencia, grant TIN2007-30838-E, Junta de Andalucí a, grant RES. 2/07-OC, Universidad de Málaga, Diputación Provincial de Málaga, Patronato de Turismo de la Costa del Sol, Ayuntamiento de Málaga, Ayuntamiento de Torremolinos, European Society for Fuzzy Logic and Technology, EUSFLAT, IEEE Computational Intelligence Society.

[131]
P. Julián, J. Medina, G. Moreno, and M. Ojeda-Aciego. Efficient thresholded tabulation for fuzzy query answering. In Foundations of reasoning under uncertainty, pages 125-141. Springer-Verlag, 2010. [ bib | http ]
Fuzzy logic programming represents a flexible and powerful declarative paradigm amalgamating fuzzy logic and logic programming, for which there exists different promising approaches described in the literature. In this paper we propose an improved fuzzy query answering procedure for the so called multi-adjoint logic programming approach, which avoids the re-evaluation of goals and the generation of useless computations thanks to the combined use of tabulation with thresholding techniques. The general idea is that, when trying to perform a computation step by using a given program rule R, we firstly analyze if such step might contribute to reach further significant solutions (non tabulated yet). When it is the case, it is possible to avoid a useless computation step via a rule R by using thresholds and filters based on the truth degree of R, as well as a safe, accurate and dynamic estimation of the maximum truth degree associated to its body.

[130]
A. Burrieza, E. Muñoz, and M. Ojeda-Aciego. Closeness and distance relations in order of magnitude qualitative reasoning via PDL. Lecture Notes in Computer Science, 5988:71-80, 2010. [ bib | http | .pdf ]
The syntax, semantics and an axiom system for an extension of Propositional Dynamic Logic (PDL) for order of magnitude qualitative reasoning which formalizes the concepts of closeness and distance is introduced in this paper. In doing this, we use some of the advantages of PDL: firstly, we exploit the possibility of constructing complex relations from simpler ones for defining the concept of closeness and other programming commands such as while ... do and repeat ... until; secondly, we employ its theoretical support in order to show that the satisfiability problem is decidable. Moreover, the specific axioms of our logic have been obtained from the minimal set of formulas needed in our definition of qualitative sum of small, medium and large numbers. We also present some of the advantages of our approach on the basis of an example.

[129]
I. P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. Congruence relations on some hyperstructures. Annals of Mathematics and Artificial Intelligence, 56(3-4):361-370, 2009. [ bib | http | .pdf ]
In this work we study the structure of the set of congruences on several hyperstructures with one and two (hyper-)operations. On the one hand, we show sufficient conditions guaranteeing that the set of congruences of an nd-groupoid forms a complete lattice (which, in turn, is a sublattice of the lattice of equivalence relations on the nd-groupoid). On the other hand, we focus on the study of the congruences on a multilattice; specifically, we prove that the set of congruences on an m-distributive multilattice forms a complete lattice and, moreover, show that the classical relationship between homomorphisms and congruences can be adequately adapted to work with multilattices under suitable restrictions.

[128]
U. Straccia, M. Ojeda-Aciego, and C.V. Damásio. On fixed-points of multi-valued functions on complete lattices and their application to generalized logic programs. SIAM J on Computing, 38(5):1881-1911, 2009. [ bib | http | .pdf ]
Unlike monotone single-valued functions, multivalued mappings may have zero, one, or (possibly infinitely) many minimal fixed-points. The contribution of this work is twofold. First, we overview and investigate the existence and computation of minimal fixed-points of multivalued mappings, whose domain is a complete lattice and whose range is its power set. Second, we show how these results are applied to a general form of logic programs, where the truth space is a complete lattice. We show that a multivalued operator can be defined whose fixed-points are in one-to-one correspondence with the models of the logic program.

[127]
N. Madrid and M. Ojeda-Aciego. On the measure of incoherence in extended residuated logic programs. In IEEE Intl Conf on Fuzzy Systems (FUZZ-IEEE'09), pages 598-603, 2009. [ bib | http | .pdf ]
In this paper we continue analyzing the introduction of negation into the framework of residuated logic programming; specifically, we focus on extended programs, in which strong negation is introduced. The classical approach to extended logic programs consists in considering negated literals as new, independent, ones and, then apply the usual monotonic approach (based on the fix-point semantics and the TP operator); if the least fix-point so obtained is inconsistent, then the approach fails and no meaning is attached to the program. This paper introduces several approaches to considering consistence (under the term coherence) into a fuzzy setting, and studies some of their properties.

[126]
J. Medina and M. Ojeda-Aciego. Taming non-commutativity in the framework of multi-adjoint concept lattices. In IASTED Conf on Artificial Intelligence and Soft Computing, pages 99-106, 2009. [ bib | .pdf ]
Sometimes, in real applications, we have to consider the use of non-commutative operators. However, it is interesting to be able to “balance" of “soften" the non-commutative character of the involved operators.

There exist some approaches to the construction of concept lattices based on non-commutative conjunctors L×L->L , but are based on the fact that the supports (or carriers) of the fuzzy subsets of both objects and attributes have to coincide.

Our contribution in this work is to present sufficient conditions in order to be able to construct concepts in a generalized fuzzy context in which the domain of the underlying conjunctors can be L1×L2 with L1<>L2.

[125]
I. P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. On congruences and homomorphisms on some non-deterministic algebras. In Intl Conf on Fuzzy Computation, pages 59-67, 2009. [ bib | .pdf ]
Starting with the underlying motivation of developing a general theory of L-fuzzy sets where L is a multilattice (a particular case of non-deterministic algebra), we study the relationship between the crisp notions of congruence, homomorphism and substructure on some non-deterministic algebras which have been used in the literature, i.e. hypergroups, and join spaces. Moreover, we provide suitable extensions of these notions to the fuzzy case.

[124]
I. P. Cabrera, P. Cordero, and M. Ojeda-Aciego. Fuzzy logic, soft computing, and applications. Lecture Notes in Computer Science, 5517:236-244, 2009. [ bib | http | .pdf ]
We survey on the theoretical and practical developments of the theory of fuzzy logic and soft computing. Specifically, we briefly review the history and main milestones of fuzzy logic (in the wide sense), the more recent development of soft computing, and finalise by presenting a panoramic view of applications: from the most abstract to the most practical ones.

[123]
J. Medina and M. Ojeda-Aciego. On the representation theorem of multi-adjoint concept lattices. In Intl Fuzzy Systems Association World Congress IFSA'09, pages 1091-1095, 2009. [ bib | .pdf ]
Formal concept analysis has become an important and appealing research topic. There exist a number of different fuzzy extensions of formal concept analysis and of its representation theorem, which gives conditions for a complete lattice in order to be isomorphic to a concept lattice. In this paper we concentrate on the study of operational properties of the mappings α and β required in the representation theorem.

[122]
O. Krídlo and M. Ojeda-Aciego. On the L-fuzzy generalization of Chu correspondences. In Computational Methods in Mathematics, Science, and Engineering, pages 608-617, 2009. Position paper. [ bib | .pdf ]
In this position paper, we focus on the framework of Chu correspondences extending Mori's approach to formal concept analysis by proposing suitable definitions of the required concepts in an L-fuzzy environment.

[121]
I. P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. On congruences, ideals and homomorphisms over multilattices. In EUROFUSE Workshop Preference Modelling and Decision Analysis, pages 299-304, 2009. [ bib | .pdf ]
In this paper, we focus on the notions of congruence, ideal and homomorphism on the generalized structure of multilattice. We provide suitable definitions of these notions in order to guarantee the classical relationship between these concepts.

[120]
N. Madrid and M. Ojeda-Aciego. On coherence and consistence in fuzzy answer set semantics for residuated logic programs. Lect. Notes in Computer Science, 5571:60-67, 2009. [ bib | http | .pdf ]
In this work we recall the first steps towards the definition of an answer set semantics for residuated logic programs with negation, and concentrate on the development of relationships between the notions of coherence and consistence of an interpretation.

[119]
A. Burrieza, A. Mora, M. Ojeda-Aciego, and E Orlowska. An implementation of a dual tableaux system for order-of-magnitude qualitative reasoning. Intl J on Computer Mathematics, 86:1852-1866, 2009. [ bib | http | .pdf ]
Logic programming has been used as a natural framework to automate deduction in the logic of order-of-magnitude reasoning. Specifically, we introduce a Prolog implementation of the Rasiowa-Sikorski proof system associated to the relational translation Re(OM) of the multimodal logic of order-of-magnitude qualitative reasoning OM.

[118]
P. Julián-Iranzo, G. Moreno, J. Medina, and M. Ojeda-Aciego. Thresholded tabulation in a fuzzy logic setting. Electronic Notes in Theoretical Computer Science, 248:115-130, 2009. [ bib | http | .pdf ]
Fuzzy logic programming represents a flexible and powerful declarative paradigm amalgamating fuzzy logic and logic programming, for which there exists different promising approaches described in the literature. In this paper we propose an improved fuzzy query answering procedure for the so called multi-adjoint logic programming approach, which avoids the re-evaluation of goals and the generation of useless computations thanks to the combined use of tabulation with thresholding techniques. The general idea is that, when trying to perform a computation step by using a given program rule R, we firstly analyze if such step might contribute to reach further significant solutions (non tabulated yet). When it is the case, it is possible to avoid a useless computation step via a rule R by using thresholds and filters based on the truth degree of R, as well as a safe, accurate and dynamic estimation of the maximum truth degree associated to its body.

[117]
I.P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego. Fuzzy congruence relations on nd-groupoids. Intl J on Computer Mathematics, 86:1684-1695, 2009. [ bib | http | .pdf ]
In this work we introduce the notion of fuzzy congruence relation on an nd-groupoid and study conditions on the nd-groupoid which guarantee a complete lattice structure on the set of fuzzy congruence relations. The study of these conditions allowed to construct a counterexample to the statement that the set of fuzzy congruences on a hypergroupoid is a complete lattice.

[116]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. Formal concept analysis via multi-adjoint concept lattices. Fuzzy Sets and Systems, 160(2):130-144, 2009. [ bib | http | .pdf ]
We investigate the use of multilattices as the set of truth-values underlying a general fuzzy logic programming framework. On the one hand, some theoretical results about ideals of a multilattice are presented in order to provide an ideal-based semantics; on the other hand, a restricted semantics, in which interpretations assign elements of a multilattice to each propositional symbol, is presented and analysed.

[115]
N. Madrid and M. Ojeda-Aciego. Towards a fuzzy answer set semantics for residuated logic programs. In Proc of WI-IAT'08. Workshop on Fuzzy Logic in the Web, pages 260-264, 2008. [ bib | http | .pdf ]
In this work we introduce the first steps towards the def- inition of an answer set semantics for residuated logic pro- grams with negation.

[114]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. Relating generalized concept lattices with concept lattices for non-commutative conjunctors. Applied Mathematics Letters, 21(12):1296-1300, 2008. [ bib | http | .pdf ]
Generalized concept lattices have been recently proposed to deal with uncertainty or incomplete information as a non-symmetric generalization of the theory of fuzzy formal concept analysis. On the other hand, concept lattices have been defined as well in the framework of fuzzy logics with non-commutative conjunctors. The contribution of this paper is to prove that any concept lattice for non- commutative fuzzy logic can be interpreted inside the framewok of generalized con- cept lattices, specifically, it is isomorphic to a sublattice of the cartesian product of two generalized concepts lattices.

[113]
P. Cordero, G. Gutiérrez, J. Martínez, M. Ojeda-Aciego, and I. de las Peñas. Congruence relations on multilattices. In Intl FLINS Conference on Computational Intelligence in Decision and Control, FLINS'08, pages 139-144, 2008. [ bib | .pdf ]
We focus on a possible generalisation of the theory of congruences on a lattice to a more general framework. In this paper, we prove that the set of congruences on an m-distributive multilattice forms a complete lattice and, moreover, show that the classical relationship between homomorphisms and congruences can be adequately adapted to work with multilattices.

[112]
P. Cordero, G. Gutiérrez, J. Martínez, M. Ojeda-Aciego, and I. de las Peñas. Fuzzy congruence relations on nd-groupoids. In Intl Conference on Mathematical Methods in Science and Engineering, CMMSE'08, pages 151-159, 2008. [ bib | .pdf ]
In this work we introduce the notion of fuzzy congruence relation on an nd- groupoid and study conditions on the nd-groupoid which guarantee a complete lattice structure on the set of fuzzy congruence relations. The study of these conditions allowed to construct a counterexample to the statement that the set of fuzzy congruences on a hypergroupoid is a complete lattice.

[111]
A. Burrieza, A. Mora, M. Ojeda-Aciego, and E. Orlowska. Implementing a relational system for order of magnitude reasoning. In Intl Conference on Mathematical Methods in Science and Engineering, CMMSE'08, pages 93-102, 2008. [ bib | .pdf ]
This work concentrates on the automated deduction of logics of order-of-magnitude reasoning. Specifically, a Prolog implementation is presented for the Rasiowa- Sikorski proof system associated to the relational translation Re(OM) of the mul- timodal logic of qualitative order-of-magnitude reasoning OM.

[110]
P. Cordero, G. Gutiérrez, J. Martínez, M. Ojeda-Aciego, and I. de las Peñas. Congruence relations on hypergroupoids and nd-groupoids. In XIV Spanish Conference on Fuzzy Logic and Technology, pages 127-132, 2008. [ bib | .pdf ]
In this work we prove that the set of congruences on an nd-groupoid under suitable conditions is a complete lattice which is a sublattice of the lattice of equivalence relations on the nd-groupoid. The study of these conditions allowed to construct a counterexample to the statement that the set of (fuzzy) congruences on a hypergroupoid is a complete lattice.

[109]
N. Madrid and M. Ojeda-Aciego. Towards an answer set semantics for residuated logic programs. In XIV Spanish Conference on Fuzzy Logic and Technology, pages 23-28, 2008. [ bib | .pdf ]
In this work we introduce the first steps towards the definition of an answer set semantics for residuated logic programs with negation.

[108]
A. Burrieza, E. Muñoz, and M. Ojeda-Aciego. A propositional dynamic logic approach for order-of-magnitude reasoning. Lect. Notes in Artificial Intelligence, 5290:11-20, 2008. [ bib | http | .pdf ]
We introduce a Propositional Dynamic Logic for order of magnitude reasoning in order to formalize qualitative operations of sum and product. This new logic has enough expressive power to consider, for example, the concept of closeness, and to study some interesting proper- ties for the qualitative operations, together with the logical definability of these properties. Finally, we show the applicability of our approach on the basis of some examples.

[107]
P. Julián-Iranzo, G. Moreno, J. Medina, and M. . Ojeda-Aciego. Combining tabulation and thresholding techniques for executing multi-adjoint logic programs. In Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU'08, pages 505-512, 2008. [ bib | .pdf ]
Multi-adjoint logic programming represents an extremely flexible attempt for fuzzifying logic programming, where the classical SLD-resolution principle has been extended to cope with imperfect information. In this paper we propose an enhanced tabulation-based query answering procedure, which avoids the generation of useless computations via thresholding techniques.

[106]
Manuel Ojeda-Aciego, Siegfried Gottwald, and Petr Hájek. Preface to “Mathematical and Logical Foundations of Soft Computing". Fuzzy Sets and Systems, 159(10):1129-1130, 2008. [ bib | http ]
[105]
P. Eklund, M.A. Galán, J. Medina, M. Ojeda-Aciego, and A. Valverde. Powersets of terms and composite monads. Fuzzy Sets and Systems, 158(23):2552-2574, 2007. [ bib | http | .pdf ]
Generalisation of the foundational basis for many-valued logic programming builds upon generalised terms in the form of powersets of terms. A categorical approach involving set and term functors as monads allows for a study of monad compositions that provide variable substitutions and compositions thereof. In this paper, substitutions and unifiers appear as constructs in Kleisli categories related to particular composed powerset term monads. Specifically, we show that a frequently used similarity-based approach to fuzzy unification is compatible with the categorical approach, and can be adequately extended in this setting; also some examples are included in order to illuminate the definitions.

[104]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. On reachability of minimal models of multilattice-based logic programming. Lect. Notes in Artificial Intelligence, 4827:271-282, 2007. [ bib | http | .pdf ]
In this paper some results are obtained regarding the existence and reachability of minimal fixed points for multiple-valued functions on a multilattice. The concept of inf-preserving multi-valued function is introduced, and shown to be a sufficient condition for the existence of minimal fixed point; then, we identify a sufficient condition granting that the immediate consequence operator for multilattice-based fuzzy logic programs is sup-preserving and, hence, computes minimal models in at most ω iterations.

[103]
A. Burrieza, E. Muñoz, and M. Ojeda-Aciego. A logic for order of magnitude reasoning with negligibility, non-closeness and distance. Lect. Notes in Artificial Intelligence, 4788:210-219, 2007. [ bib | http | .pdf ]
This paper continues the research line on the multimodal logic of qualitative reasoning; specifically, it deals with the introduction of the notions non-closeness and distance. These concepts allow us to consider qualitative sum of medium and large numbers. We present a sound and complete axiomatization for this logic, together with some of its advantages by means of an example.

[102]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. Concept lattices under non-commutative conjunctors are generalized concept lattices. In Intl Conference on Fuzzy Logic and Technology, vol. II, pages 209-212, 2007. [ bib | .pdf ]
Generalized concept lattices have been recently proposed to deal with uncertainty or incomplete information as a non-symmetric generalization of the theory of fuzzy formal concept analysis. On the other hand, concept lattices have been defined as well in the framework of fuzzy logics with non- commutative conjunctors. The contribution of this paper is to prove that any concept lattice for non-commutative fuzzy logic can be interpreted inside the framewok of generalized concept lattices, specifically, it is isomorphic to a sublattice of the cartesian product of two generalized concepts lattices.

[101]
C.V. Damásio, J. Medina, and M. Ojeda-Aciego. Termination of logic programs with imperfect information: applications and query procedure. Journal of Applied Logic, 5(3):435-458, 2007. [ bib | http | .pdf ]
A general logic programming framework allowing for the combination of several adjoint lattices of truth-values is presented. The language is sorted, enabling the combination of several reasoning forms in the same knowledge base. The contribution of the paper is two-fold: on the one hand, sufficient conditions guaranteeing termination of all queries for the fix-point semantics for a wide class of sorted multi-adjoint logic programs are presented and related to some well-known probability-based formalisms; in addition, we specify a general non-deterministic tabulation goal-oriented query procedure for sorted multi-adjoint logic programs over complete lattices. We prove its soundness and completeness as well as independence of the selection ordering. We apply the termination results to probabilistic and fuzzy logic programming languages, enabling the use of the tabulation proof procedure for query answering.

[100]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. A fixed-point theorem for multi-valued functions with application to multilattice-based logic programming. Lect. Notes in Artificial Intelligence, 4578:37-44, 2007. [ bib | http | .pdf ]
This paper presents a computability theorem for fixed points of multi-valued functions defined on multilattices, which is later used in order to obtain conditions which ensure that the immediate consequence operator computes minimal models of multilattice-based logic programs in at most ? iterations.

[99]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. On multi-adjoint concept lattices: definition and representation theorem. Lect. Notes in Computer Science, 4390:197-209, 2007. [ bib | http | .pdf ]
Several fuzzifications of formal concept analysis have been proposed to deal with uncertainty or incomplete information. In this paper, we focus on the new paradigm of multi-adjoint concept lattices which embeds different fuzzy extensions of concept lattices, our main result being the representation theorem of this paradigm. As a consequence of this theorem, the representation theorems of the other paradigms can be proved more directly. Moreover, the multi-adjoint paradigm enriches the language providing greater flexibility to the user.

[98]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. Fuzzy logic programming via multilattices. Fuzzy Sets and Systems, 158(6):674-688, 2007. [ bib | http | .pdf ]
We investigate the use of multilattices as the set of truth-values underlying a general fuzzy logic programming framework. On the one hand, some theoretical results about ideals of a multilattice are presented in order to provide an ideal-based semantics; on the other hand, a restricted semantics, in which interpretations assign elements of a multilattice to each propositional symbol, is presented and analysed.

[97]
A. Burrieza, M. Ojeda-Aciego, and E. Orlowska. Relational approach to order of magnitude reasoning. Lect. Notes in Computer Science, 4342:105-124, 2006. [ bib | http | .pdf ]
[96]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. Multi-adjoint concept lattices from a non-commutative perspective. In 13th Spanish Congress on Fuzzy Logic and Technology, pages 147-152, 2006. [ bib | .pdf ]
[95]
C. Damásio, J. Medina, and M. Ojeda-Aciego. A tabulation procedure for first-order residuated logic programs: soundness, completeness and optimisations. In Proc. IEEE Congress on Computational Intelligence (section Fuzzy Systems), pages 9576-9583, 2006. [ bib | http | .pdf ]
[94]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. On the ideal semantics of multilattice-based logic programs. In Information Processing and Management of Uncertainty, IPMU'06, pages 463-470, 2006. [ bib | .pdf ]
[93]
C. Damásio, J. Medina, and M. Ojeda-Aciego. A tabulation procedure for first-order residuated logic programs. In Information Processing and Management of Uncertainty, IPMU'06, pages 225-232, 2006. [ bib | .pdf ]
[92]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. Retículos de conceptos multi-adjuntos. In Campus Multidisciplinar de Percepción e Inteligencia, pages 751-762, 2006. [ bib | .pdf ]
[91]
A. Burrieza, E. Muñoz, and M. Ojeda-Aciego. Order of magnitude qualitative reasoning with bidirectional negligibility. Lect. Notes in Artificial Intelligence, 4177:370-378, 2006. [ bib | http | .pdf ]
[90]
J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño. Multi-lattices as a basis for generalized fuzzy logic programming. Lect. Notes in Artificial Intelligence, 3849:61-70, 2006. [ bib | http | .pdf ]
[89]
J. Medina, E. Mérida-Casermeiro, and M. Ojeda-Aciego. A neural implementation of multi-adjoint logic programs via sf-homogeneous programs. Mathware & Soft Computing, XII:199-216, 2005. [ bib | http | .pdf ]
[88]
A. Burrieza and M. Ojeda-Aciego. On the modal logic of order-of-magnitude qualitative reasoning: a tableau calculus. In EPIA'05, pages 33-37. IEEE Press, 2005. [ bib | http | .pdf ]
[87]
J. Medina, M. Ojeda-Aciego, and J. Ruiz. Fuzzy logic programming via multilattices: first results and prospects. In Proc of Lógica Fuzzy & Soft Computing, pages 19-26. Thomson, 2005. [ bib ]
[86]
A. Burrieza and M. Ojeda-Aciego. A multimodal logic approach to order of magnitude qualitative reasoning with comparability and negligibility relations. Fundamenta Informaticae, 68:21-46, 2005. [ bib | http | .pdf ]
[85]
J. Medina, E. Mérida-Casermeiro, and M. Ojeda-Aciego. Interval-valued neural multi-adjoint logic programs. Lect. Notes in Computer Science, 3561:521-530, 2005. [ bib | http | .pdf ]
[84]
J. Medina, E. Mérida-Casermeiro, and M. Ojeda-Aciego. Decomposing ordinal sums in neural multi-adjoint logic programs. Lect. Notes in Artificial Intelligence, 3315:717-726, 2004. [ bib | http | .pdf ]
[83]
M. Ojeda-Aciego and A. Valverde. tascpl: TAS solver for Classical Propositional Logic. Lect. Notes in Artificial Intelligence, 3229:731-735, 2004. [ bib | .pdf ]
[82]
C.V. Damásio, J. Medina, and M. Ojeda-Aciego. Sorted multi-adjoint logic programs: termination results and applications. Lect. Notes in Artificial Intelligence, 3229:260-273, 2004. [ bib | .pdf ]
[81]
C.V. Damásio, J. Medina, and M. Ojeda-Aciego. A tabulation proof procedure for residuated logic programming. In European Conference on Artificial Intelligence, volume 110 of Frontiers in Artificial Intelligence and Applications, pages 808-812, 2004. [ bib | .pdf ]
[80]
C.V. Damásio, J. Medina, and M. Ojeda-Aciego. A termination theorem for sorted multi-adjoint logic programming. In 12th Spanish Congress on Fuzzy Logic and Technology, 2004. [ bib | .pdf ]
[79]
J. Medina and M. Ojeda-Aciego. Extended homogenization for multi-adjoint logic programs. In 12th Spanish Congress on Fuzzy Logic and Technology, 2004. [ bib | .pdf ]
[78]
J. Medina, E. Mérida-Casermeiro, and M. Ojeda-Aciego. A neural implementation of multi-adjoint logic programming. Journal of Applied Logic, 2/3:301-324, 2004. [ bib | http | .pdf ]
[77]
J. Medina and M. Ojeda-Aciego. Multi-adjoint logic programming. In Information Processing and Management of Uncertainty, IPMU'04, pages 823-828, 2004. Invited talk of special session on Logic Programming with Imperfect Information. [ bib | .pdf ]
[76]
C.V. Damásio, J. Medina, and M. Ojeda-Aciego. Termination results for sorted multi-adjoint logic programs. In Information Processing and Management of Uncertainty, IPMU'04, pages 1879-1886, 2004. [ bib | .pdf ]
[75]
M. Ojeda-Aciego. Lógica, matemática, deducción automática. La Gaceta de la R.S.M.E., 8(1):93-119, 2005. [ bib | .pdf ]
[74]
J. Medina, M. Ojeda-Aciego, and P. Vojtáš. Similarity-based unification: a multi-adjoint approach. Fuzzy Sets and Systems, 146(1):43-62, 2004. [ bib | http | .pdf ]
[73]
P. Eklund, M.A. Galán, J. Medina, M. Ojeda-Aciego, and A. Valverde. Similarities between powersets of terms. Fuzzy Sets and Systems, 144(1):213-225, 2004. [ bib | http | .pdf ]
[72]
M. Ojeda-Aciego. España entra a formar parte de ERCIM. La Gaceta de la R.S.M.E., 7(1):37-52, 2004. [ bib | .pdf ]
[71]
M. Ojeda-Aciego, P. Vojtáš, and S. Zadrożny. Guest editorial. Kybernetika, 39(5):509-510, 2003. [ bib ]
[70]
A. Burrieza and M. Ojeda-Aciego. A multimodal logic approach to order of magnitude qualitative reasoning. Lect. Notes in Artificial Intelligence, 3040:66-75, 2003. [ bib | .pdf ]
[69]
J. Medina, M. Ojeda-Aciego, and P. Vojtáš. Towards biresiduated multi-adjoint logic programming. In Spanish Conference on Artificial Intelligence, pages 608-617. Lect. Notes in Artificial Intelligence 3040, 2003. [ bib | .pdf ]
[68]
J. Medina and M. Ojeda-Aciego. Homogenizing multi-adjoint logic programs. In Intl Conference on Fuzzy Logic and Technology, pages 640-644, 2003. [ bib | .pdf | .pdf ]
[67]
C.V. Damásio and M. Ojeda-Aciego. On termination of a tabulation procedure for residuated logic programming. In 6th Intl Workshop on Termination, WST'03, pages 40-43, 2003. [ bib | .pdf ]
[66]
A. Burrieza and M. Ojeda-Aciego. La incidencia de las ciencias formales en computación. In A. Diéguez, editor, Tecnociencia y Cultura a comienzos del siglo xxi, pages 161-177. Servicio de Publicaciones de la Universidad de Málaga, 2004. [ bib ]
[65]
J. Medina, E. Mérida-Casermeiro, and M. Ojeda-Aciego. A neural approach to diagnosis based on extended logic programming. In 8th Conf. Engineering Applications of Neural Networks, EANN'03, 2003. [ bib | .pdf ]
[64]
J. Medina, E. Mérida-Casermeiro, and M. Ojeda-Aciego. A neural approach to extended logic programs. In 7th Intl Work Conference on Artificial and Natural Neural Networks, IWANN'03, pages 654-661. Lect. Notes in Computer Science 2686, 2003. [ bib | .pdf ]
[63]
P. Eklund, M.A. Galán, J. Medina, M. Ojeda-Aciego, and A. Valverde. Set functors, L-fuzzy set categories and generalized terms. Computers and Mathematics with Applications, 43:693-705, 2002. [ bib | http | .pdf ]
[62]
M. Ojeda-Aciego, I. P. de Guzmán, G. Brewka, and L.M. Pereira. Preface to the special issue on “logics in artificial intelligence". Studia Logica, 72:3-5, 2002. [ bib | http ]
[61]
G. Gutiérrez, I. P. de Guzmán, J. Martínez, M. Ojeda-Aciego, and A. Valverde. Satisfiability testing for Boolean formulas using Δ-trees. Studia Logica, 72:33-60, 2002. [ bib | http | .pdf ]
[60]
S. Krajči, R. Lencses, J. Medina, M. Ojeda-Aciego, A. Valverde, and P. Vojtáš. Non-commutativity and expressive deductive logic databases. In Logics in Artificial Intelligence, JELIA'02, pages 149-160. Lect. Notes in Artificial Intelligence 2424, 2002. [ bib | .pdf ]
[59]
S. Krajči, R. Lencses, J. Medina, M. Ojeda-Aciego, and P. Vojtáš. A similarity-based unification model for flexible querying. In Flexible querying and answering systems, FQAS'02, pages 263-273. Lect. Notes in Artificial Intelligence 2522, 2002. [ bib | .pdf ]
[58]
J. Medina, E. Mérida-Casermeiro, and M. Ojeda-Aciego. A neural approach to abductive multi-adjoint reasoning. In AI - Methodologies, Systems, Applications. AIMSA'02. Lect. Notes in Computer Science 2443, 2002. 213-222. [ bib | .pdf ]
[57]
I.P. de Guzmán, M. Ojeda-Aciego, and A. Valverde. Restricted Δ-trees in multiple-valued logics. In AI - Methodologies, Systems, Applications. AIMSA'02, pages 223-232. Lect. Notes in Computer Science 2443, 2002. [ bib | .pdf ]
[56]
I.P. de Guzmán, M. Ojeda-Aciego, and A. Valverde. Restricted Δ-trees and reduction theorems in multiple-valued logics. In Advances in Artificial Intelligence, IBERAMIA'02, pages 161-171. Lect. Notes in Artificial Intelligence 2527, 2002. [ bib | .pdf ]
[55]
J. Medina and M. Ojeda-Aciego. A new approach to completeness for multi-adjoint logic programming. In 9th Information Processing and Management of Uncertainty in Knowledge-Based Systems Conference, IPMU 2002, 2002. [ bib | .pdf ]
[54]
P. Eklund, M.A. Galán, J. Medina, M. Ojeda Aciego, and A. Valverde. A framework for unification using powersets of terms. In 9th Information Processing and Management of Uncertainty in Knowledge-Based Systems Conference, IPMU 2002, 2002. [ bib | .pdf ]
[53]
J. Medina, E. Mérida-Casermeiro, and M. Ojeda-Aciego. Multi-adjoint logic programming: a neural net approach. In Logic Programming. ICLP'02, page 468. Lect. Notes in Computer Science 2401, 2002. [ bib | .pdf ]
[52]
P. Eklund and M.. Ojeda-Aciego, editors. Preface to the special issue “Unification in non-classical logics", volume 66.5. Electronic Notes in Theoretical Computer Science, 2002. [ bib | http ]
[51]
P. Eklund, M.A. Galán, J. Medina M.. Ojeda-Aciego, and A. Valverde. A categorical approach to unification of generalized terms. In Unification in non-classical logics, volume 66.5. Electronic Notes in Theoretical Computer Science, 2002. [ bib | http ]
[50]
J. Medina, M.. Ojeda-Aciego, and P. Vojtáš. Similarity-based multi-adjoint unification. In Unification in non-classical logics, volume 66.5. Electronic Notes in Theoretical Computer Science, 2002. [ bib | http ]
[49]
J. Medina and M.. Ojeda-Aciego. On first-order multi-adjoint logic programming. In 11th Spanish Congress on Fuzzy Logic and Technology, 2002. [ bib ]
[48]
J. Medina, E. Mérida-Casermeiro, and M. Ojeda-Aciego. Multi-adjoint abduction via neural nets. In 11th Spanish Congress on Fuzzy Logic and Technology, 2002. [ bib ]
[47]
J. Medina, M. Ojeda-Aciego, and P. Vojtáš. Similarity-based unification. In Intl Conference on Fuzzy Logic and Technology, 2001. [ bib ]
[46]
G. Aguilera, I. P. de Guzmán, M. Ojeda-Aciego, and A. Valverde. Reductions for non-clausal theorem proving. Theoretical Computer Science, 266(1/2):81-112, 2001. [ bib | http | .pdf ]
[45]
J. Medina, M. Ojeda-Aciego, and P. Vojtáš. A procedural semantics for multi-adjoint logic programming. In Progress in Artificial Intelligence, EPIA'01, pages 290-297. Lect. Notes in Artificial Intelligence 2258, 2001. [ bib | .pdf ]
[44]
J. Medina, M. Ojeda-Aciego, and P. Vojtáš. A multi-adjoint logic approach to abductive reasoning. In Logic Programming, ICLP'01, pages 269-283. Lect. Notes in Computer Science 2237, 2001. [ bib | .pdf ]
[43]
J. Medina, M. Ojeda-Aciego, and P. Vojtáš. Multi-adjoint logic programming with continuous semantics. Lect. Notes in Artificial Intelligence, 2173:351-364, 2001. [ bib | http | .pdf ]
[42]
P. Eklund, M.A. Galán, J. Medina, M.. Ojeda-Aciego, and A. Valverde. Composing submonads. In Proc. 31st IEEE Intl. Symposium on Multiple-Valued Logic, pages 367-372. IEEE-CS, 2001. [ bib ]
[41]
P. Eklund, M.A. Galán, J. Medina, M.. Ojeda-Aciego, and A. Valverde. Set functors and L-fuzzy set categories: towards a fuzzy programming paradigm. In 2nd Intl ICSC Symposium on Fuzzy Logic and Applications, 2001. [ bib ]
[40]
J. Medina, M. Ojeda-Aciego, and P. Vojtáš. A completeness theorem for multi-adjoint logic programming. In Proc. FUZZ-IEEE'01. The 10th IEEE International Conference on Fuzzy Systems, IEEE Press, 2001. [ bib | .pdf ]
[39]
S. Merino and M. Ojeda-Aciego. Automatización del diseño de torres. In Primeras Jornadas sobre Avances Científicos en Ingeniería Industrial y Civil, 2001. [ bib ]
[38]
M. Ojeda-Aciego, I. P. de Guzmán, G. Brewka, and L.M. Pereira, editors. Logics in Artificial Intelligence, volume 1919 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 2000. [ bib ]
[37]
G. Gutiérrez, I. P. de Guzmán, J. Martínez, , M. Ojeda-Aciego, and A. Valverde. Reduction theorems for Boolean formulas using Δ-trees. In Proc. of JELIA 2000, pages 179-192. Lect. Notes in Artif. Intelligence 1919, 2000. [ bib ]
[36]
P. Eklund, M. A. Galán, M. Ojeda-Aciego, and A. Valverde. Set functors and generalised terms. In Proc. of IPMU 2000, volume III of Information Processing and Management of Uncertainty in Knowledge-based Systems, pages 1595-1599, 2000. [ bib | .pdf ]
[35]
P. Eklund, M. A. Galán, M. Ojeda-Aciego, and A. Valverde. Monad composition and generalised terms. In 21st Linz Seminar on Fuzzy Set Theory, 2000. [ bib ]
[34]
P. Eklund, M. A. Galán, J. Medina, M. Ojeda-Aciego, and A. Valverde. Generalised terms and composition of monads. In Proc. of ESTYLF 2000, Spanish Congress on Fuzzy Logic and Technology, pages 155-160, 2000. [ bib ]
[33]
P. Eklund, M. Ángeles Galán, J. Medina, M. Ojeda Aciego, and A. Valverde. A graphical approach to monad compositions. In Proceedings of MFCSIT 2000, Mathematical Foundations of Computer Science and Information Technology, 2000. [ bib | .html ]
[32]
G. Aguilera, I. P. de Guzmán, M. Ojeda Aciego, and A. Valverde. Master theses for providing feedback to the logic classroom. In 1st Intl Congress on Tools for Teaching Logic, 2000. [ bib ]
[31]
G. Aguilera, J. de Medina, M. Ojeda Aciego, and A. Valverde. Generalized branching rules for negation normal forms. In 1st Joint Mathematical European-Arabic Conference, 2000. [ bib ]
[30]
G. Gutiérrez, I. P. de Guzmán, J. Martínez, M. Ojeda-Aciego, and A. Valverde. Representing Boolean formulas by using trees of implicants and implicates. In Proc. of CSI 2000, 2000. [ bib | .pdf ]
[29]
I. P. de Guzmán, M. Ojeda-Aciego, and A. Valverde. Reducing signed propositional formulas. Soft Computing, 2(4):157-166, 1999. [ bib | .pdf ]
[28]
I. P. de Guzmán, M. Ojeda-Aciego, and A. Valverde. Implicates and reduction techniques for temporal logics. Annals of Mathematics and Artificial Intelligence, 27:2-23, 1999. [ bib | .pdf ]
[27]
I. P. de Guzmán, M. Ojeda-Aciego, and A. Valverde. Multiple-valued tableaux with Δ-reductions. In Proc. of the Intl. Conf. on Artificial Intelligence, ICAI'99, pages 177-183. C.S.R.E.A., 1999. [ bib | .pdf ]
[26]
S. Cárdenas, M. Ojeda-Aciego, and S. Sánchez. Construcciones geométricas con ordenador. In Congreso Nacional de Informática Educativa, 1999. [ bib ]
[25]
M. Ojeda-Aciego and S. Sánchez. Una experiencia geométrica para estudiantes de ingeniería. In Jornadas de Aprendizaje y Enseñanza de las Matemáticas, 1999. [ bib ]
[24]
I. P. de Guzmán, M. Ojeda-Aciego, and A. Valverde. Implicates and reduction techniques for temporal logics. In Proc. of JELIA'98, pages 309-323. Lect. Notes in Artif. Intelligence 1489, 1998. [ bib | .pdf ]
[23]
G. Aguilera, I. P. de Guzmán, and M. Ojeda-Aciego. A new reduction-based theorem prover for 3-valued logic. Mathware & Soft Computing, 4(2):99-127, 1997. [ bib ]
[22]
G. Aguilera, I. P. de Guzmán, and M. Ojeda-Aciego. Dp-distributions: a new efficiency strategy for the TAS reduction method. In Proceedings of Logic Colloquium'97, 1997. [ bib ]
[21]
G. Aguilera, I. P. de Guzmán, and M. Ojeda-Aciego. Model building in 3-valued logic using the TAS reduction paradigm. In Proceedings of the IJCAI'97 workshop on Model-based Automated Reasoning, 1997. [ bib ]
[20]
G. Aguilera, I. P. de Guzmán, and M. Ojeda-Aciego. The TAS reduction method in multiple-valud logics. In Dagstuhl seminar: multiple valued logic, 1997. [ bib ]
[19]
M. Ojeda-Aciego and I. P. de Guzmán. Lógica para la Computación (II). Ágora, 1997. [ bib ]
[18]
C. Pareja, M. Ojeda-Aciego, Á. Andeyro, and C. Rossi. Desarrollo de algoritmos y técnicas de programación en PASCAL. Ra-Ma, 1997. [ bib ]
[17]
M. Ojeda-Aciego, I. P. de Guzmán, and M. Enciso. Theorem proving for temporal logic using the TAS paradigm. In Proceedings of Iberamia'96, Cholula (Mexico), 1996. [ bib ]
[16]
M. Enciso, I. P. de Guzmán, J. Moncada, and M. Ojeda-Aciego. Executing intensional logic with the TAS tool. In Proceedings of AGP'96, 1996. [ bib ]
[15]
M. Ojeda-Aciego. Formal methods for normalization in first-order logic using the TAS methodology. In 2nd Conference on Multiple-Valued Logics for Computer Science Applications, 1996. [ bib ]
[14]
I.P. de Guzmán and M. Ojeda-Aciego. TAS methods in first-order logic. In Logic Colloquium'96, 1996. [ bib ]
[13]
I.P. de Guzmán and M. Ojeda-Aciego. A new approach to the translation into normal form. In Foundations of Mathematics and Computer Science, 1996. [ bib ]
[12]
I. P. de Guzmán, M. Ojeda, and A. Valverde. A formal identification between tuples and lists with an application to list-arithmetic categories. Acta Informatica, 32:61-78, 1995. [ bib ]
[11]
G. Aguilera, I. P. de Guzmán, and M. Ojeda-Aciego. Increasing the efficiency of automated theorem proving. Journal of Applied Non-Classical Logics, 5(1):9-29, 1995. [ bib ]
[10]
G. Aguilera, I. P. de Guzmán, and M. Ojeda-Aciego. A new general approach to ATPs. In Proceedings of KI-15, Workshop on Computational Propositional Logic, Bielefeld (Germany), September 1995. [ bib ]
[9]
I. P. de Guzmán and M. Ojeda-Aciego. The GIMAC project. In Proceedings of COST action 15: Many-valued Logics for Computer Science Applications, Lyon (Francia), dic 1995. [ bib ]
[8]
G. Aguilera, I. P. de Guzmán, and M. Ojeda-Aciego. Automated model building via syntactic trees transformations. In CADE workshop on Automated Model Building, pages 4-10, Nancy (France), June 1994. [ bib ]
[7]
G. Aguilera, I. P. de Guzmán, José L. Galán, and M. Ojeda-Aciego. TAS-D++ vs tablas semánticas. In GULP-PRODE '94 Joint Conference on Declarative Programming, Valencia, September 1994. [ bib ]
[6]
G. Aguilera, I. P. de Guzmán, José L. Galán, and M. Ojeda-Aciego. Using TAS-D++ for inferences. In Proceedings of Iberamia'94, pages 44-59, Caracas (Venezuela), October 1994. [ bib ]
[5]
G. Aguilera, I. P. de Guzmán, and M. Ojeda-Aciego. TAS-D++ syntactic trees transformations for automated theorem proving. Lect. Notes in Artif. Intelligence 838, pages 198-216, September 1994. [ bib ]
[4]
C. Pareja, M. Ojeda-Aciego, and Á. Andeyro. Introducción a la Informática. Ed. Complutense, 1994. [ bib ]
[3]
M. Ojeda-Aciego. Cálculo para la Computación (I). Ágora, 1993. [ bib ]
[2]
G. Aguilera, I. P. de Guzmán, and M. Ojeda-Aciego. Un algoritmo eficiente y paralelo para la transformación a forma normal conjuntiva. In Programación Declarativa, pages 275-290, Blanes (Spain), September 1993. [ bib ]
[1]
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