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Quantified Equilibrium Logic and Foundations for Answer Set Programs

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Logic Programming (ICLP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5366))

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Abstract

QHT is a first-order super-intuitionistic logic that provides a foundation for answer set programming (ASP) and a useful tool for analysing and transforming non-ground programs. We recall some properties of QHT and its nonmonotonic extension, quantified equilibrium logic (QEL). We show how the proof theory of QHT can be used to extend to non-ground programs previous results on the completeness of θ-subsumption. We also establish a reduction of QHT to classical logic and show how this can be used to obtain and extend classical encodings for concepts such as the strong equivalence of programs and theories. We pay special attention to a class of general (disjunctive) logic programs that capture all universal theories in QEL.

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Author information

Authors and Affiliations

  1. Universidad Rey Juan Carlos, Madrid, Spain

    David Pearce

  2. Universidad de Málaga, Málaga, Spain

    Agustín Valverde

Authors
  1. David Pearce
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  2. Agustín Valverde
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Editor information

Editors and Affiliations

  1. Clayton School of Information Technology, Monash University, Australia

    Maria Garcia de la Banda

  2. Department of Computer Science, New Mexico State University, NM 88003, Las Cruces, USA

    Enrico Pontelli

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Pearce, D., Valverde, A. (2008). Quantified Equilibrium Logic and Foundations for Answer Set Programs. In: Garcia de la Banda, M., Pontelli, E. (eds) Logic Programming. ICLP 2008. Lecture Notes in Computer Science, vol 5366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89982-2_46

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  • DOI: https://doi.org/10.1007/978-3-540-89982-2_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89981-5

  • Online ISBN: 978-3-540-89982-2

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