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Semantically-Guided Goal-Sensitive Reasoning: Inference System and Completeness

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Abstract

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.

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Notes

  1. An early forerunner of CDCL was the semantic tree method with lemma generation (cf. pages 284–288 in [53]).

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Acknowledgments

An abstract of an early version of this work was presented at the Meeting of the IFIP Working Group 1.6 on Rewriting at the Sixth Federated Logic Conference (FLoC) at the Vienna Summer of Logic in July 2014. This article was completed when the first author was an international fellow at the Computer Science Laboratory of SRI International in Menlo Park, and also during a visit at Microsoft Research in Redmond: the support of both institutions is gratefully acknowledged. We thank the reviewers for their comments that helped us improve our manuscript.

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  1. Dipartimento di Informatica, Università degli Studi di Verona, Strada Le Grazie 15, 37134, Verona, Italy

    Maria Paola Bonacina

  2. Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    David A. Plaisted

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  1. Maria Paola Bonacina
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Bonacina, M.P., Plaisted, D.A. Semantically-Guided Goal-Sensitive Reasoning: Inference System and Completeness. J Autom Reasoning 59, 165–218 (2017). https://doi.org/10.1007/s10817-016-9384-2

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