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.
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Baumgartner, P., Brüning, S. A Disjunctive Positive Refinement of Model Elimination and its Application to Subsumption Deletion. Journal of Automated Reasoning 19, 205–262 (1997). https://doi.org/10.1023/A:1005812703468
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DOI: https://doi.org/10.1023/A:1005812703468