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Belief revision, minimal change and relaxation: A general framework based on satisfaction systems, and applications to description logics

Marc Aiguier, Jamal Atif, Isabelle Bloch & Céline Hudelot

Artificial Intelligence 256 (C):160-180 (2018)

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Morphologic for knowledge dynamics: revision, fusion and abduction.Isabelle Bloch, Jérôme Lang, Ramón Pino Pérez & Carlos Uzcátegui - 2023 - Journal of Applied Non-Classical Logics 33 (3):421-466.details Several tasks in artificial intelligence require the ability to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper, we exploit the algebraic framework of mathematical morphology in the context of propositional logic and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based on a semantic approach, that have an intuitive interpretation and that are formally well behaved, to perform revision, fusion and abduction. Computation (...) Download Export citation Bookmark 1 citation
Abstract Categorical Logic.Marc Aiguier & Isabelle Bloch - 2023 - Logica Universalis 17 (1):23-67.details We present in this paper an abstract categorical logic based on an abstraction of quantifier. More precisely, the proposed logic is abstract because no structural constraints are imposed on models (semantics free). By contrast, formulas are inductively defined from an abstraction both of atomic formulas and of quantifiers. In this sense, the proposed approach differs from other works interested in formalizing the notion of abstract logic and of which the closest to our approach are the institutions, which in addition to (...) Download Export citation Bookmark
A Closeness- and Priority-Based Logical Study of Social Network Creation.Sonja Smets & Fernando R. Velázquez-Quesada - 2020 - Journal of Logic, Language and Information 29 (1):21-51.details This paper is part of an on-going programme on the study of the logical aspects of social network formation. It recalls the so-called social network model, discussing the properties of a notion of closeness between agents ; then introduces an extended social network model in which different agents might assign different values to different traits, discussing the properties of the notion of weighted closeness that arises. These notions are used to define social network creation operations by means of a threshold (...) Download Export citation Bookmark 1 citation
Logical dual concepts based on mathematical morphology in stratified institutions: applications to spatial reasoning.Marc Aiguier & Isabelle Bloch - 2019 - Journal of Applied Non-Classical Logics 29 (4):392-429.details Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and sets of (...) Download Export citation Bookmark 2 citations

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