Axiomatisation of constraint systems to specify a tableaux calculus modulo theories

In this paper we explore a proof-theoretic approach to the combination of generic proof-search and theory-specific procedures, in presence of quantifiers. Forming the basis of tableaux methods, the sequent calculus is refined with meta-variables (a.k.a existential variables or free variables) to delay the choice of witnesses, and parameterised by theory-specific features based on a system of constraints for meta-variables. An axiomatisation of these features is given, so that the soundness and completeness of the sequent calculus with meta-variables can be generically proved (with respect to the sequent calculus where the choice of witnesses is not delayed). We then describe a theory-generic proof-search implementation, that is parameterised by a theory-specific module whose specification is given by the above axiomatisation.