Analysing and Extending Well-Founded and Partial Stable Semantics Using Partial Equilibrium Logic

  • Pedro Cabalar
  • Sergei Odintsov
  • David Pearce
  • Agustín Valverde
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4079)


In [4] a nonmonotonic formalism called partial equilibrium logic (PEL) was proposed as a logical foundation for the well-founded semantics (WFS) of logic programs. PEL consists in defining a class of minimal models, called partial equilibrium (p-equilibrium), inside a non-classical logic called HT 2. In [4] it was shown that, on normal logic programs, p-equilibrium models coincide with Przymusinki’s partial stable (p-stable) models. This paper begins showing that this coincidence still holds for the more general class of disjunctive programs, so that PEL can be seen as a way to extend WFS and p-stable semantics to arbitrary propositional theories. We also study here the problem of strong equivalence for various subclasses of p-equilibrium models, investigate transformation rules and nonmonotonic inference, and consider a reduction of PEL to equilibrium logic. In addition we examine the behaviour of PEL on nested logic programs and its complexity in the general case.


Logic Program Stable Model Double Negation Disjunctive Program Partial Equilibrium Model 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Pedro Cabalar
    • 1
  • Sergei Odintsov
    • 2
  • David Pearce
    • 3
  • Agustín Valverde
    • 4
  1. 1.Corunna UniversityCorunnaSpain
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia
  3. 3.Universidad Rey Juan CarlosMadridSpain
  4. 4.University of MálagaMálagaSpain

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