## Section: New Results

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

Participants : Damien Rouhling, Stéphane 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.