Topological Reasoning and The Logic of Knowledge

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. Department of Mathematics, Indiana University, Bloomington IN 47405 USA yDepartment of Mathematics, Indiana University, Bloomington IN 47405 USA zDepartments of Computer Science, Mathematics and Philosophy, CUNY Graduate Center, New York, NY 10036 USA, and Department of Compu...

• Type: Conference
• Year: 1992
• Where: TARK
• Authors: Lawrence S. Moss, Rohit Parikh
• Keywords: Automated Reasoning, Bimodal Logic, Computer Science, Indiana University, TARK 1992