Quantified Equilibrium Logic and Foundations for Answer Set Programs

  • Authors:
  • David Pearce;Agustín Valverde

  • Affiliations:
  • Universidad Rey Juan Carlos, Madrid, Spain;Universidad de Málaga, Málaga, Spain

  • Venue:
  • ICLP '08 Proceedings of the 24th International Conference on Logic Programming
  • Year:
  • 2008

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Abstract

QHT is a first-order super-intuitionistic logic that provides afoundation for answer set programming (ASP) and a useful tool foranalysing and transforming non-ground programs. We recall someproperties of QHT and its nonmonotonic extension, quantifiedequilibrium logic (QEL). We show how the proof theory of QHT can beused to extend to non-ground programs previous results on thecompleteness of θ-subsumption. We also establish a reductionof QHT to classical logic and show how this can be used to obtainand extend classical encodings for concepts such as the strongequivalence of programs and theories. We pay special attention to aclass of general (disjunctive) logic programs that capture alluniversal theories in QEL.