Topological reasoning and the logic of knowledge

Annals of Pure and Applied Logic 78 (1-3):73-110 (1996)
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Abstract

We present a bimodal logic suitable for formalizing reasoning about points and sets, and also states of the world and views about them. The most natural interpretation of the logic is in subset spaces , and we obtain complete axiomatizations for the sentences which hold in these interpretations. In addition, we axiomatize the validities of the smaller class of topological spaces in a system we call topologic . We also prove decidability for these two systems. Our results on topologic relate early work of McKinsey on topological interpretations of S4 with recent work of Georgatos on topologic. Some of the results of this paper were presented at the 1992 conference on Theoretical Aspects of Reasoning about Knowledge

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Rohit Parikh
CUNY Graduate Center

Citations of this work

Neighborhood Semantics for Modal Logic.Eric Pacuit - 2017 - Cham, Switzerland: Springer.
The Logic of Framing Effects.Francesco Berto & Aybüke Özgün - 2023 - Journal of Philosophical Logic 1:1-24.

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