Conference paper
Conference paper accepted
26/07/22/09:27
F. Pérez-Gámez, P. Cordero, M. Enciso, A. Mora, M. Ojeda-Aciego. Grading unknown information via an intuitionistic approah. European Symposium on Computational Intelligence and Mathematics (ESCIM), Naples, Italy, 2022.
ABSTRACT Information is not always precise and exact and, in many cases, some data are missed or unknown. To manage this data, fuzzy logic introduces a set of (infinitely many) values between the two Boolean truth values. Other authors use a three-valued approach, by adding an intermediate value to the set of Boolean truth-values. We propose a formal framework strongly based on Atanassov fuzzy sets, associating each proposition with a pair of degrees characterizing our knowledge about the two truth-values, since this logic does not include the law of the excluded middle.
Our starting point is the crisp Formal Concept Analysis, which provides a formal framework for knowledge representation and reasoning. Information is described by means of a binary relation characterizing the relationship among a set of objects and a set of attributes. We extend the crisp framework considering a pair of degrees for each element in the relation.
Formal concept analysis provides a twofold representation of knowledge: the so-called concept lattice and the implication set. In this paper we choose the second option since it better provides a symbolic manipulation of the information. Here, we introduce the syntax and semantics for a new intuitionistic implication. This notion of implication allows a further definition of an intuitionistic logic to manage this kind of information with great expressive power, but avoiding the complexity problems of classical propositional logic.
ABSTRACT Information is not always precise and exact and, in many cases, some data are missed or unknown. To manage this data, fuzzy logic introduces a set of (infinitely many) values between the two Boolean truth values. Other authors use a three-valued approach, by adding an intermediate value to the set of Boolean truth-values. We propose a formal framework strongly based on Atanassov fuzzy sets, associating each proposition with a pair of degrees characterizing our knowledge about the two truth-values, since this logic does not include the law of the excluded middle.
Our starting point is the crisp Formal Concept Analysis, which provides a formal framework for knowledge representation and reasoning. Information is described by means of a binary relation characterizing the relationship among a set of objects and a set of attributes. We extend the crisp framework considering a pair of degrees for each element in the relation.
Formal concept analysis provides a twofold representation of knowledge: the so-called concept lattice and the implication set. In this paper we choose the second option since it better provides a symbolic manipulation of the information. Here, we introduce the syntax and semantics for a new intuitionistic implication. This notion of implication allows a further definition of an intuitionistic logic to manage this kind of information with great expressive power, but avoiding the complexity problems of classical propositional logic.
Conference paper accepted
08/07/22/12:27
F.J. Valverde-Albacete, C. Peláez-Moreno, I.P. Cabrera, P. Cordero, M. Ojeda-Aciego. Can FCA Provide a Framework for Artificial General Intelligence? Workshop What can FCA do for Artificial Intelligence? (FCA4AI@IJCAI-ECAI'22), Vienna, 2022.
ABSTRACT This paper is an attempt at bridging two strains of research being developed by the authors: a theory of information flows to subserve intelligence and a theory of affordances for the modelling of Embodied, Embedded, Extended and Enacted Computational Intelligence as pro- vided by FCA. We list previous successes, present challenges, and future avenues of research that suggest themselves.
ABSTRACT This paper is an attempt at bridging two strains of research being developed by the authors: a theory of information flows to subserve intelligence and a theory of affordances for the modelling of Embodied, Embedded, Extended and Enacted Computational Intelligence as pro- vided by FCA. We list previous successes, present challenges, and future avenues of research that suggest themselves.
Conference paper accepted
18/06/21/13:30
N. Madrid, M. Ojeda-Aciego. Measuring Consistency of Fuzzy Logic Theories. Proc. of the Spanish Conference on Fuzzy Logic and Technology, Málaga, 2021.
ABSTRACT 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 paper starts with a short survey of different ways to define the notion of inconsistency in fuzzy logic systems. As a result, we provide a first notion of inconsistency by means of the absence of models. Subsequently, we define two measures of consistency that belong purely to the fuzzy paradigm; in the sense that both measures coincide with the crisp notion of consistency when the set of truth values is $\{0,1\}$. Accordingly, we can state that the two provided measures of consistence are notions of consistence based on degrees, bringing back the spirit of fuzzy logic into the notion of consistency.
ABSTRACT 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 paper starts with a short survey of different ways to define the notion of inconsistency in fuzzy logic systems. As a result, we provide a first notion of inconsistency by means of the absence of models. Subsequently, we define two measures of consistency that belong purely to the fuzzy paradigm; in the sense that both measures coincide with the crisp notion of consistency when the set of truth values is $\{0,1\}$. Accordingly, we can state that the two provided measures of consistence are notions of consistence based on degrees, bringing back the spirit of fuzzy logic into the notion of consistency.
Conference papers accepted
26/05/21/10:32
N. Madrid, M. Ojeda-Aciego. Approaching the square of oppositions in terms of the f-indexes of inclusion and contradiction. Proc. of the 19th World Congress of the International Fuzzy Systems Association and 12th Conference of the European Society for Fuzzy Logic and Technology, Bratislava, 2021.
ABSTRACT We continue analyzing the properties of f-inclusion and f-contradiction, and provide an alternative interpretation of the square of opposition.
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero and E. Muñoz-Velasco. Closure systems as a fuzzy extension of meet-subsemilattices. Proc. of the 19th World Congress of the International Fuzzy Systems Association and 12th Conference of the European Society for Fuzzy Logic and Technology, Bratislava, 2021.
ABSTRACT An extension of the notion of closure system is introduced adapting the notion of meet-subsemilattice to a complete fuzzy lattice. Results relating closure operators and closure systems in the classical case are extended properly to this framework. Then, this definition is proved to be equivalent to the most used definition given by Belohlávek on the fuzzy powerset lattice.
ABSTRACT We continue analyzing the properties of f-inclusion and f-contradiction, and provide an alternative interpretation of the square of opposition.
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero and E. Muñoz-Velasco. Closure systems as a fuzzy extension of meet-subsemilattices. Proc. of the 19th World Congress of the International Fuzzy Systems Association and 12th Conference of the European Society for Fuzzy Logic and Technology, Bratislava, 2021.
ABSTRACT An extension of the notion of closure system is introduced adapting the notion of meet-subsemilattice to a complete fuzzy lattice. Results relating closure operators and closure systems in the classical case are extended properly to this framework. Then, this definition is proved to be equivalent to the most used definition given by Belohlávek on the fuzzy powerset lattice.
Conference paper accepted
15/03/21/09:11
D. López-Rodríguez, P. Cordero, M. Enciso, Á. Mora. Clustering and identification of core implications. Int Con on Formal Concept Analysis (ICFCA), Strasbourg, 2021.
ABSTRACT FCA exhaustively uses the notion of cluster, by grouping attributes and objects and also providing a strong algebraic structure to them by means of the concept lattice. Our proposal explores how we can cluster implications. This work opens a research line in the direction of studying the knowledge inside the clusters computed from the Duquenne-Guigues basis. Some alternative measures to induce the clusters are analyzed, taking into account the information that directly appears in the appearance and in the semantics of the implications. This work also allows us to show to the FCA community the fcaR package, having the main methods of FCA and of the Simplification Logic. The paper ends with a motivation of the potential applications of performing clustering on the implications.
ABSTRACT FCA exhaustively uses the notion of cluster, by grouping attributes and objects and also providing a strong algebraic structure to them by means of the concept lattice. Our proposal explores how we can cluster implications. This work opens a research line in the direction of studying the knowledge inside the clusters computed from the Duquenne-Guigues basis. Some alternative measures to induce the clusters are analyzed, taking into account the information that directly appears in the appearance and in the semantics of the implications. This work also allows us to show to the FCA community the fcaR package, having the main methods of FCA and of the Simplification Logic. The paper ends with a motivation of the potential applications of performing clustering on the implications.