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Journal of Logic and Computation Advance Access originally published online on September 1, 2006
Journal of Logic and Computation 2007 17(1):53-82; doi:10.1093/logcom/exl018
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Anytime Approximations of Classical Logic from Above

Marcelo Finger

Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, São Paulo, Brazil. Email: mfinger{at}ime.usp.br

Renata Wassermann

Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, São Paulo, Brazil. Email: renata{at}ime.usp.br


  Abstract

In this article we present Formula , a family of logics that is useful to disprove propositional formulas by means of an anytime approximation process. The systems follows the paradigm of a parameterized family of logics established by Schaerf's and Cadoli's system S1. We show that Formula inherits several of the nice properties of S1, while presenting several attractive new properties. The family Formula deals with the full propositional language, has a complete tableau proof system which provides for incremental approximations; furthermore, it constitutes a full approximation of classical logic from above, with an approximation process with better relevance and locality properties than S1. When applied to clausal inference, Formula provides a strong simplification method. An application of Formula to model-based diagnosis is presented, demonstrating how the solution to this problem can benefit from the use of Formula approximations.

Keywords: Automated reasoning; approximate reasoning; theorem proving; satisfiability


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