Abstract : We present a sound and complete ordered resolution calculus for first-order clauses with straight dismatching constraints. The extended clause language is motivated by our first-order theorem proving approach through approximation and refinement. Using a clause language with straight dismatching constraints, single refinement steps do not result in a worst-case quadratic blowup in the number of clauses anymore. The refinement steps can now be represented by replacing one input clause with two equivalent clauses. We show soundness and completeness of ordered resolution with straight dismatching constraints. All needed operations on straight dismatching constraints take linear or linear logarithmic time in the size of the constraint.
https://hal.inria.fr/hal-01403206
Contributor : Stephan Merz
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Submitted on : Monday, November 28, 2016 - 4:53:35 PM
Last modification on : Tuesday, February 19, 2019 - 3:40:04 PM
Long-term archiving on : Tuesday, March 21, 2017 - 9:42:59 AM
Andreas Teucke, Christoph Weidenbach. Ordered Resolution with Straight Dismatching Constraints. 5th Workshop on Practical Aspects of Automated Reasoning (PAAR 2016), 2016, Coimbra, Portugal. pp.95-109. ⟨hal-01403206⟩
