Parametrized semantics of logic programs: a unifying framework

  • Authors:

  • Yann Loyer;Nicolas Spyratos;Daniel Stamate

  • Affiliations:

  • Laboratoire PRiSM, Université de Versailles Saint Quentin, 45 Avenue des Etats-Unis, 78035 Versailles, France;Laboratoire de Recherche en Informatique, UMR 8623, Université de Paris Sud, Bat. 490, 91405 Orsay, France;Department of Computing, Goldsmiths, University of London, New Cross, London SE14 6NW, UK

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2003

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Abstract

The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms that are rule heads and whose logical values cannot be inferred from the rules. For example, the well founded semantics corresponds to the assumption that every such atom is false, while the Kripke-Kleene semantics corresponds to the assumption that every such atom is unknown. In this paper, we propose to unify and extend this assumption-based approach by introducing parameterized semantics for logic programs. The parameter holds the value that one assumes for all rule heads whose logical values cannot be inferred from the rules. We work within multi-valued logic with bilattice structure, and we consider the class of logic programs defined by Fitting.Following Fitting's approach, we define an operator that allows us to compute the parameterized semantic, and to compare and combine semantics obtained for different values of the parameter. We show that our approach captures and extends the usual semantics of conventional logic programs thereby unifying their computation.