Axiomatic constraint systems for proof search modulo theories

International audienceGoal-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

A Proof-Theoretic Perspective on SMT-Solving for Intuitionistic Propositional Logic

Claessen and R\uf3sen have recently presented an automated theorem prover, intuit, for intuitionistic propositional logic which utilises a SAT-solver. We present a sequent calculus perspective of the theory underpinning intuit by showing that it implements a generalisation of the implication-left rule from the sequent calculus LJT, also known as G4ip and popularised by Roy Dyckhoff