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Conflict resolution: a first-order resolution calculus with decision literals and conflict-driven clause learning. (English) Zbl 1425.68379

Summary: This paper defines the (first-order) conflict resolution calculus: an extension of the resolution calculus inspired by techniques used in modern Sat-solvers. The resolution inference rule is restricted to (first-order) unit propagation and the calculus is extended with a mechanism for assuming decision literals and with a new inference rule for clause learning, which is a first-order generalization of the propositional conflict-driven clause learning procedure. The calculus is sound (because it can be simulated by natural deduction) and refutationally complete (because it can simulate resolution), and these facts are proven in detail here.

MSC:

68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
03B35 Mechanization of proofs and logical operations
68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
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