Polyhedral semantics and the tractable approximation of Łukasiewicz infinitely-valued logic
Author:
Finger Marcelo1,
Preto Sandro1
Affiliation:
1. Institute of Mathematics and Statistics , University of São Paulo, São Paulo, 05508-090, Brazil
Abstract
Abstract
In this work, we present polyhedral semantics as a means to tractably approximate Łukasiewicz infinitely-valued logic (Ł$_{\infty}$). As Ł$_{\infty}$ is an expressive multivalued propositional logic whose decision problem is NP-complete, we show how to to obtain an approximation for this problem providing a family of multivalued logics over the same language as Ł$_{\infty}$. Each element of the family is associated to a polynomial-time linear program, thus providing a tractable way of deciding each intermediate step. We also investigate properties of the logic system derived from polyhedral semantics and the details of an algorithm for the approximation process.
Publisher
Oxford University Press (OUP)
Subject
Logic,Hardware and Architecture,Arts and Humanities (miscellaneous),Software,Theoretical Computer Science
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