Logic Programming

Volume 2237 of the series Lecture Notes in Computer Science pp 212-226


Ultimate Well-Founded and Stable Semantics for Logic Programs with Aggregates

  • Marc DeneckerAffiliated withDept. of Computer Science, K.U.Leuven
  • , Nikolay PelovAffiliated withDept. of Computer Science, K.U.Leuven
  • , Maurice BruynoogheAffiliated withDept. of Computer Science, K.U.Leuven

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In this paper, we propose an extension of the well-founded and stable model semantics for logic programs with aggregates. Our approach uses Approximation Theory, a fixpoint theory of stable and well-founded fixpoints of non-monotone operators in a complete lattice. We define the syntax of logic programs with aggregates and define the immediate consequence operator of such programs. We investigate the well-founded and stable semantics generated by Approximation Theory. We show that our approach extends logic programs with stratified aggregation and that it correctly deals with well-known benchmark problems such as the shortest path program and the company control problem.