A Disjunctive Positive Refinement of Model Elimination and its Application to Subsumption Deletion

  • Authors:

  • Peter Baumgartner;Stefan Brüning

  • Affiliations:

  • Universität Koblenz, Institut für Informatik, Rheinau 1, 56075 Koblenz, Germany. e-mail: peter@informatik.uni-koblenz.de;Technische Hochschule Darmstadt, Fachbereich Informatik, Intellektik, Alexanderstr. 10, 64283 Darmstadt, Germany. e-mail: stebr@intellektik.informatik.th-darmstadt.de

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 1997

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Abstract

The Model Elimination (ME) calculus is a refutationally complete,goal-oriented calculus for first-order clause logic. In this article, weintroduce a new variant called disjunctive positive ME (DPME); it improveson Plaisted’s positive refinement of ME in that reduction steps areallowed only with positive literals stemming from clauses having at leasttwo positive literals (so-called disjunctive clauses). DPME is motivated byits application to various kinds of subsumption deletion: in order to applysubsumption deletion in ME equally successful as in resolution, it iscrucial to employ a version of ME that minimizes ancestor context (i.e., thenecessary A-literals to find a refutation). DPME meets this demand. Wedescribe several variants of ME with subsumption, the most important onesbeing ME with backward and forward subsumption and theT*-Context Check. We compare their pruning power, also takinginto consideration the well-known regularity restriction. All proofs aresupplied. The practicability of our approach is demonstrated with experiments.