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Journal of Logic and Computation Advance Access published online on September 1, 2006
Journal of Logic and Computation, 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 Papers

Anytime Approximations of Classical Logic from Above

Marcelo Finger 1 * and Renata Wassermann 1 *

1 Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, São Paulo, Brazil

* To whom correspondence should be addressed.
Marcelo Finger, E-mail: mfinger{at}ime.usp.br
Renata Wassermann, E-mail: renata{at}ime.usp.br


  Abstract

In this article we present s1, 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 s1 inherits several of the nice properties of S1, while presenting several attractive new properties. The family s1 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, s1 provides a strong simplification method. An application of s1 to model-based diagnosis is presented, demonstrating how the solution to this problem can benefit from the use of s1 approximations.

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