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Logical dual concepts based on mathematical morphology in stratified institutions: applications to spatial reasoning

Logical dual concepts based on mathematical morphology in stratified institutions: applications... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

Logical dual concepts based on mathematical morphology in stratified institutions: applications to spatial reasoning

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Logical dual concepts based on mathematical morphology in stratified institutions: applications to spatial reasoning

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...
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Publisher
Taylor & Francis
Copyright
© 2019 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.2019.1668678
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Applied Non-Classical Logics – Taylor & Francis

Published: Oct 2, 2019

Keywords: Stratified institutions; mathematical morphology; dual operators; spatial reasoning

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