Pseudo-Metrics on the set of abstract logic formulas
by
Guojun Wang
Institute of Mathematics, Shaanxi Normal University

Let F be the set of all abstract formulas in two valued propositional logic and \Omega the set consisting of all valuations of F. The Lebesgue measure is introduced on \Omega and every formula of F then has a tautology degree therefrom. The concept of similarity degree among formulas is also introduced. Finally, a pseudo-metric among formulas is defined by means of similarity degrees and it is proved that the pseudo-metric space F has no isolated point and hence certain approximate reasoning theory can be developed on F. Moreover, the method employed above can be extended to establish pseudo-metrics on the sets of formulas of different type of multiple valued logics and offer a unified approximate reasoning theory on them.

Institute of Mathematics, Shaanxi Normal Unviersity, Xi'an 710062, China

Date received: April 5, 2001

Copyright © 2001 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 # cagw-08.