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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 ... (Update)
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BibTeX entry: (Update)
@article{ dabrowski96topological,
author = "Andrew Dabrowski and Lawrence S. Moss and Rohit Parikh",
title = "Topological Reasoning and the Logic of Knowledge",
journal = "Annals of Pure and Applied Logic",
volume = "78",
number = "1-3",
pages = "73-110",
year = "1996",
url = "citeseer.ist.psu.edu/278.html" }
Citations (may not include all citations):264 Knowledge and common knowledge in a distributed environment - Halpern, Moses - 1984
194 Knowledge and Belief (context) - Hintikka - 1962
114 Logics of Time and Computation (context) - Goldblatt - 1987
76 How processes learn (context) - Chandy, Misra - 1986
73 Topology via Logic (context) - Vickers - 1989
19 A Model-Theoretic Analysis of Knowledge - Fagin, Halpern et al. - 1988
17 On some completeness theorems in modal logic (context) - Makinson - 1966
2 Logics of knowledge (context) - Parikh - 1984
1 City University of New York (context) - Georgatos, Ph - 1993
1 Knowledge theoretic properties of topological spaces (context) - Georgatos - 1994
1 Distributed computing and the logic of knowledge (context) - Parikh, Ramanujam - 1985
1 Valid Rreasoning and Visual Representation (context) - Shin - 1991
1 Reasoning about knowledge on computation trees (context) - Georgatos - 1994
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