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Journal of Logic and Computation Advance Access originally published online on April 17, 2007
Journal of Logic and Computation 2007 17(3):499-515; doi:10.1093/logcom/exm011
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Strong Negation and Equivalence in the Safe Belief Semantics

Magdalena Ortiz and Mauricio Osorio

Universidad de las Américas, Sta. Catarina Mártir, Cholula, Puebla. 72820 México.

E-mail: ortiz{at}kr.tuwien.ac.at; osoriomauri{at}gmail.com

Received 28 November 2005.


  Abstract

The safe belief semantics uses intermediate logics to define an extension of answer sets to all propositional formulas, but only considering one kind of negation. In this work we extend safe beliefs adding the strong negation connective. The main feature of our extension is that strong negation can occur before any formula, and not only at the atomic level. We give results concerning the relation between strong negation extensions of intermediate logics and safe beliefs and consider the way in which strong negation can be eliminated from any formula while preserving its semantics. We also propose two new notions of equivalence: substitution equivalence and contextualized equivalence. We prove that they are both more general than strong equivalence and, for propositional formulas where strong negation may occur at the non-atomic level, substitution equivalence captures a notion of equivalence that cannot be captured by strong equivalence alone.

Keywords: Nelson logics; answer sets; intermediate logics; equivalence; constructive negation


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