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Section: New Results

Axiomatization of constraint systems for first-order reasoning modulo a theory

Participants : Damien Rouhling, St├ęphane Graham-Lengrand, Assia Mahboubi, Jean-Marc Notin, Mahfuza Farooque.

This result is part of a work in theorem proving, whose purpose is to provide a theoretical basis for the handling of quantifiers in presence of a theory for which we have specific decision procedures. Inspired by the way first-order unifiers are generated and propagated in automated reasoning techniques such as tableaux methods, we sought to generalise these mechanisms to the presence of a theory: We introduced a axiomatic notion of constraint system and a sequent calculus introducing meta-variables and propagating constraints. We then identified the axioms that should be satisfied by the theory's decision procedure, in order for the sequent calculus to be sound and complete. This provides the theoretical basis for the development of Psyche 2.0. This result is submitted for publication.