Axiomatic constraint systems for proof search modulo theories

Abstract : Goal-directed proof search in first-order logic uses meta-variables to delay the choice of witnesses; substitutions for such variables are produced when closing proof-tree branches, using first-order unification or a theory-specific background reasoner. This paper investigates a generalisation of such mechanisms whereby theory-specific constraints are produced instead of substitutions. In order to design modular proof-search procedures over such mechanisms, we provide a sequent calculus with meta-variables, which manipulates such constraints abstractly. Proving soundness and completeness of the calculus leads to an axiomatisation that identifies the conditions under which abstract constraints can be generated and propagated in the same way unifiers usually are. We then extract from our abstract framework a component interface and a specification for concrete implementations of background reasoners.
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https://hal.inria.fr/hal-01107944
Contributor : Assia Mahboubi <>
Submitted on : Wednesday, January 21, 2015 - 8:39:53 PM
Last modification on : Saturday, March 30, 2019 - 1:34:36 AM

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Damien Rouhling, Mahfuza Farooque, Stéphane Graham-Lengrand, Jean-Marc Notin, Assia Mahboubi. Axiomatic constraint systems for proof search modulo theories. 10th International Symposium on Frontiers of Combining Systems (FroCoS'15), Sep 2015, Wroclaw, Poland. ⟨10.1007/978-3-319-24246-0_14⟩. ⟨hal-01107944⟩

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