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Characterizations for Relativized Notions of Equivalence in Answer Set Programming

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Logics in Artificial Intelligence (JELIA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3229))

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Abstract

Recent research in nonmonotonic logic programming focuses on alternative notions of equivalence. In particular, strong and uniform equivalence are both proposed as useful tools to optimize (parts of) a logic program. More specifically, given a set P of program rules and a possible optimization Q, strong (resp. uniform) equivalence requires that adding any set S of rules (resp. facts) to P and Q simultaneously results in equivalent programs, i.e., P∪ S and Q∪ S possess the same stable models. However, in practice it is often necessary to relax this condition in such a way, that dedicated internal atoms in P or Q are no longer allowed to occur in the possible extensions S. In this paper, we consider these relativized notions of both uniform and strong equivalence and provide semantical characterizations by generalizing the notions of UE- and SE-modelhood. These new characterizations capture all notions of equivalence including ordinary equivalence in a uniform way. Finally, we analyze the complexity of the introduced equivalence tests for the important classes of normal and disjunctive logic programs. As a by-product, we reduce the tests for relativized equivalences to ordinary equivalence between two programs. These reductions may serve as a basis for implementation.

Supported by the Austrian Science Fund (FWF) under project P15068-INF and by the European Commission under projects FET-2001-37004 WASP and IST-2001-33570 INFOMIX.

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Authors and Affiliations

  1. Institut für Informationssysteme 184/3, Technische Universität Wien, Favoritenstraße 9-11, A-1040, Vienna, Austria

    Stefan Woltran

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  1. Stefan Woltran
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Editors and Affiliations

  1. CENTRIA, Universidade Nova de Lisboa, Portugal

    Jóse Júlio Alferes

  2. Departamento de Informática, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    João Leite

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Woltran, S. (2004). Characterizations for Relativized Notions of Equivalence in Answer Set Programming. In: Alferes, J.J., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2004. Lecture Notes in Computer Science(), vol 3229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30227-8_16

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  • DOI: https://doi.org/10.1007/978-3-540-30227-8_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23242-1

  • Online ISBN: 978-3-540-30227-8

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