Modal logics for topological spaces.
Item
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Title
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Modal logics for topological spaces.
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Identifier
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AAI9325096
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identifier
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9325096
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Creator
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Georgatos, Konstantinos.
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Contributor
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Adviser: Rohit Parikh
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Date
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1993
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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We present two bimodal systems, MP and MP*, for reasoning about knowledge and effort.;Knowledge is interpreted as all true statements common to a set of possible worlds which represents our view. Effort corresponds to increase of information and translates to a restriction of our view. Such restrictions are parameterized by the worlds in our view and therefore are neighborhood restrictions. The semantics of these logics consist of pairs of points and their neighborhoods. In this spatial setting basic topological and computation concepts are naturally expressed which make these systems ideal for studying computing knowledge by set-theoretic means.;The system MP was introduced and proven complete for the class of sets containing arbitrary neighborhoods by Larry Moss and Rohit Parikh. In this thesis, MP*, an extension of MP, is introduced and proven complete for various class of spaces closed under unions and intersections, among them topological spaces. We also present necessary and sufficient conditions under which a Kripke frame can be turned into a set-theoretic model of ours. Among our results is the finite model property and decidability for MP*. In addition we present the algebraic models of these systems and discuss further work.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
