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Modal Logics Based on Mathematical Morphology for Qualitative Spatial Reasoning

Journal of Applied Non-Classical Logics 12 (3):399-423 (2002)

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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
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
Logic for physical space: From antiquity to present days.Marco Aiello, Guram Bezhanishvili, Isabelle Bloch & Valentin Goranko - 2012 - Synthese 186 (3):619-632.details Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones (...) Download Export citation Bookmark

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