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Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation pp 125–140Cite as

Stability, Supportedness, Minimality and Kleene Answer Set Programs

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9060))

Abstract

Answer Set Programming is a widely known knowledge representation framework based on the logic programming paradigm that has been extensively studied in the past decades. The semantic framework for Answer Set Programs is based on the use of stable model semantics. There are two characteristics intrinsically associated with the construction of stable models for answer set programs. Any member of an answer set is supported through facts and chains of rules and those members are in the answer set only if generated minimally in such a manner. These two characteristics, supportedness and minimality, provide the essence of stable models. Additionally, answer sets are implicitly partial and that partiality provides epistemic overtones to the interpretation of disjunctive rules and default negation. This paper is intended to shed light on these characteristics by defining a semantic framework for answer set programming based on an extended first-order Kleene logic with weak and strong negation. Additionally, a definition of strongly supported models is introduced, separate from the minimality assumption explicit in stable models. This is used to both clarify and generate alternative semantic interpretations for answer set programs with disjunctive rules in addition to answer set programs with constraint rules. An algorithm is provided for computing supported models and comparative complexity results between strongly supported and stable model generation are provided.

This work is partially supported by the Swedish Research Council (VR) Linnaeus Center CADICS, the ELLIIT network organization for Information and Communication Technology, the Swedish Foundation for Strategic Research (CUAS Project), the EU FP7 project SHERPA (grant agreement 600958), and Vinnova NFFP6 Project 2013-01206.

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Authors and Affiliations

  1. Dept. of Computer and Information Science, Linköping University, 581 83, Linköping, Sweden

    Patrick Doherty & Andrzej Szałas

  2. Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Szałas

Authors
  1. Patrick Doherty
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  2. Andrzej Szałas
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Editors and Affiliations

  1. Institut für Informationssysteme, Technische Universität Wien, 184/3, Abteilung für wissensbasierte Systeme, Favoritenstraße 9-11, 1040, Wien, Austria

    Thomas Eiter

  2. Institut für Informatik, Abteilung Intelligente Systeme, Universität Leipzig, PF 100920, 04009, Leipzig, Germany

    Hannes Strass

  3. Department of Computer Science, University of Kentucky, 309 Davis Marksbury Building, 329 Rose Street, 40506-0633, Lexington, KY, USA

    Mirosław Truszczyński

  4. Institut für Informationssysteme, Technische Universität Wien, 184/2, Abteilung für Datenbanken und Artificial Intelligence, Favoritenstraße 9-11, 1040, Wien, Austria

    Stefan Woltran

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Doherty, P., Szałas, A. (2015). Stability, Supportedness, Minimality and Kleene Answer Set Programs. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds) Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation. Lecture Notes in Computer Science(), vol 9060. Springer, Cham. https://doi.org/10.1007/978-3-319-14726-0_9

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  • DOI: https://doi.org/10.1007/978-3-319-14726-0_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14725-3

  • Online ISBN: 978-3-319-14726-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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