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• W2977046078 abstract "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 models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, whose satisfaction is parametrised by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided." @default.
• W2977046078 created "2019-10-03" @default.
• W2977046078 creator A5063487294 @default.
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• W2977046078 date "2019-09-27" @default.
• W2977046078 modified "2023-10-15" @default.
• W2977046078 title "Logical dual concepts based on mathematical morphology in stratified institutions: applications to spatial reasoning" @default.
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• W2977046078 doi "https://doi.org/10.1080/11663081.2019.1668678" @default.
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