Topological reasoning and the logic of knowledge

Annals of Pure and Applied Logic 78 (1-3):73-110 (1996)
Rohit Parikh
CUNY Graduate Center
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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DOI 10.1016/0168-0072(95)00016-X
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References found in this work BETA

Topological Reasoning and the Logic of Knowledge.Andrew Dabrowski, Lawrence S. Moss & Rohit Parikh - 1996 - Annals of Pure and Applied Logic 78 (1-3):73-110.
On Some Completeness Theorems in Modal Logic.D. Makinson - 1966 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 12 (1):379-384.
Knowledge Theoretic Properties of Topological Spaces.Konstantinos Georgatos - 1994 - In Masuch, Michael & Polos Laszlo (eds.), Knowledge Representation and Uncertainty. Springer Verlag. pp. 147--159.

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Citations of this work BETA

Dynamic Logics of Evidence-Based Beliefs.J. Benthem & E. Pacuit - 2011 - Studia Logica 99 (1-3):61-92.
Topological Reasoning and the Logic of Knowledge.Andrew Dabrowski, Lawrence S. Moss & Rohit Parikh - 1996 - Annals of Pure and Applied Logic 78 (1-3):73-110.

View all 13 citations / Add more citations

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