Annals of Pure and Applied Logic 78 (1-3):73-110 (1996)
AbstractWe 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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References found in this work
On Some Completeness Theorems in Modal Logic.D. Makinson - 1966 - Mathematical Logic Quarterly 12 (1):379-384.
A solution of the decision problem for the Lewis systems s2 and s4, with an application to topology.J. C. C. McKinsey - 1941 - Journal of Symbolic Logic 6 (4):117-134.
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.
Knowledge Theoretic Properties of Topological Spaces.Konstantinos Georgatos - 1994 - In Masuch, Michael & Polos Laszlo (eds.), Knowledge Representation and Uncertainty. Springer Verlag. pp. 147--159.