‘Classical’ Negation in Nonmonotonic Reasoning and Logic Programming

  • Authors:

  • José Júlio Alferes;Luís Moniz Pereira;Teodor C. Przymusinski

  • Affiliations:

  • Dep. Matemática, Univ. Évora, and A.I. Centre, UNL, 2825 Monte da Caparica, Portugal, e-mail:jja@di.fct.unl.pt;A.I. Centre, Univ. Nova de Lisboa, 2825 Monte da Caparica, Portugal, e-mail:lmp@di.fct.unl.pt;Department of Computer Science, University of California, Riverside, CA 92521, U.S.A. e-mail:teodor@cs.ucr.edu

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 1998

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Abstract

Gelfond and Lifschitz were the first to point out the need for asymmetric negation in logic programming and they also proposed a specificsemantics for such negation for logic programs with the stable semantics,which they called ‘classical’. Subsequently, several researchersproposed different, often incompatible, forms of symmetric negation forvarious semantics of logic programs and deductive databases. To the best ofour knowledge, however, no systematic study of symmetric negation innon-monotonic reasoning was ever attempted in the past. In this paper weconduct such a systematic study of symmetric negation. We introduce anddiscuss two natural, yet different, definitions of symmetric negation: oneis called strong negation and the other is called explicit negation. Forlogic programs with the stable semantics, both symmetric negations coincidewith Gelfond–Lifschitz’ ‘classical negation’. Westudy properties of strong and explicit negation and their mutualrelationship as well as their relationship to default negation‘not’, and classical negation ‘¬’.We show how one can use symmetric negation to provide natural solutions tovarious knowledge representation problems, such as theory and interpretationupdate, and belief revision. Rather than to limit our discussion to somenarrow class of nonmonotonic theories, such as the class of logic programswith some specific semantics, we conduct our study so that it is applicableto a broad class of non-monotonic formalisms. In order to achieve thedesired level of generality, we define the notion of symmetric negation inthe knowledge representation framework of AutoEpistemic logic of Beliefs,introduced by Przymusinski.