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Semantically-guided goal-sensitive reasoning: inference system and completeness. (English) Zbl 1437.68189
Summary: We present a new method for clausal theorem proving, named SGGS from semantically-guided goal-sensitive reasoning. SGGS generalizes to first-order logic the conflict-driven clause learning (CDCL) procedure for propositional satisfiability. Starting from an initial interpretation, used for semantic guidance, SGGS employs a sequence of constrained clauses to represent a candidate model, instance generation to extend it, resolution and other inferences to explain and solve conflicts, amending the model. We prove that SGGS is refutationally complete and model complete in the limit, regardless of initial interpretation. SGGS is also goal sensitive, if the initial interpretation is properly chosen, and proof confluent, because it repairs the current model without undoing steps by backtracking. Thus, SGGS is a complete first-order method that is simultaneously model-based à la CDCL, semantically-guided, goal-sensitive, and proof confluent.

68V15 Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.)
03B35 Mechanization of proofs and logical operations
Full Text: DOI
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