Strong negation in well-founded and partial stable semantics for logic programs

  • Authors:

  • Pedro Cabalar;Sergei Odintsov;David Pearce

  • Affiliations:

  • Corunna University, Corunna, Spain;Sobolev Institute of Mathematics, Novosibirsk, Russia;Universidad Rey Juan Carlos, Madrid, Spain

  • Venue:
  • IBERAMIA-SBIA'06 Proceedings of the 2nd international joint conference, and Proceedings of the 10th Ibero-American Conference on AI 18th Brazilian conference on Advances in Artificial Intelligence
  • Year:
  • 2006

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Abstract

A formalism called partial equilibrium logic (PEL) has recently been proposed as a logical foundation for the well-founded semantics (WFS) of logic programs. In PEL one defines a class of minimal models, called partial equilibrium models, in a non-classical logic, HT2. On logic programs partial equilibrium models coincide with Przymusinski’s partial stable (p-stable) models, so that PEL can be seen as a way to extend WFS and p-stable semantics to arbitrary propositional theories. We study several extensions of PEL with strong negation and compare these with previous systems extending WFS with explicit negation, notably WSFX [10] and p-stable models with “classical” negation [11].