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The 12th Summer Conference on General Topology and its Applications
August 12-16, 1997
Nipissing University
North Bay, ON, Canada

Organizers
Ted Chase, Boguslaw Schreyer, Jodi Sutherland, Murat Tuncali, Stephen Watson

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Possibility Measures, Topology, and Quantitative Semantics
by
Michael Huth
Department of Computing and Information Sciences, Kansas State University
Coauthors: Reinhold Heckmann (Department of Computing and Information Sciences, Kansas State University)

Generalizing the usual predicate transformers to quantitative predicate transformers we uncover that such transformers have a mathematical dual which provides a mathematical foundation for possibility theories in Artificial Intelligence. This duality reveals formal analogies of quantitative predicates with continuous valuations. Three applications of this duality demonstrate its usefulness: we prove a universal property for the space of quantitative predicates, we characterize its inf-irreducible elements, and we show that bicontinuous lattices form a cartesian closed category.

Date received: June 26, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caao-29.