On the strong completion of logic programs

  • Phan Minh Dung
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 463)


A new completion theory for logic programming called strong completion, is introduced. Similar to the Clark's completion, the strong completion can be interpreted either in two-valued or three-valued logic. We show that
  • ⋆Two-valued strong completion specifies the stable semantics.

  • ⋆Three-valued strong completion specifies the well-founded semantics.

Since the strong completion of a logic program P is also a circumscription of P, the open problem as whether or not there exists a circumscriptive specification of a logic program P which specifies the stable semantics as well as the well-founded semantics of P, is solved.

We show that the call-consistency condition is sufficient for a logic program to have a stable model. Further we prove that the stable semantics is equivalent to the well-founded semantics if the program is strict and call-consistent.


Logic programming negation predicate completion stable models well-founded models circumscription two-valued logic three-valued logic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Phan Minh Dung
    • 1
  1. 1.Asian Institute of TechnologyDivision of Computer ScienceBangkokThailand

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