Topological reasoning and the logic of knowledge: preliminary report

Authors:
Lawrence S. Moss;Rohit Parikh
Affiliations:
Indiana University, Bloomington, IN;CUNY Graduate Center, New York, NY
Venue:
TARK '92 Proceedings of the 4th conference on Theoretical aspects of reasoning about knowledge
Year:
1992

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Abstract

What are fields of mathematics, such as probability theory, point-set topology, and combinatorics, about? When asked this, a mathematician is likely to answer that the field is about various mathematical concepts, or about the consequences of some axioms or other. Although this answer would be adequate for many purposes, it misses a deeper answer that areas of mathematics can be seen as repositories for our intuitions about several aspects of ordinary life. For example, combinatories can be seen as just the mathematical home for intuitions about activities like counting and arranging. General topology can be seen as the home for intuitions about closeness.