Splitting an Operator

An Algebraic Modularity Result and Its Application to Logic Programming
  • Joost Vennekens
  • David Gilis
  • Marc Denecker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3132)


It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different “levels”, such that the models of the entire program can be constructed by incrementally constructing models for each level. Similar results exist for other non-monotonic formalisms, such as auto-epistemic logic and default logic. In this work, we present a general, algebraic splitting theory for programs/theories under a fixpoint semantics. Together with the framework of approximation theory, a general fixpoint theory for arbitrary operators, this gives us a uniform and powerful way of deriving splitting results for each logic with a fixpoint semantics. We demonstrate the usefulness of these results, by generalizing Lifschitz and Turner’s splitting theorem to other semantics for (non-disjunctive) logic programs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Joost Vennekens
    • 1
  • David Gilis
    • 1
  • Marc Denecker
    • 1
  1. 1.Department of Computer ScienceK.U. LeuvenLeuvenBelgium

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