Section: New Results

Automated reasoning and SMT solving

Participants : Mahfuza Farooque, Stéphane Lengrand.

Automated reasoning uses a broad range of techniques whose soundness and completeness relate to the existence of proofs. The research programme of the ANR PSI project at Parsifal is to build a finer-grained connection by specifying automated reasoning techniques as the step-by-step construction of proofs, as we know it from proof theory and logic programming. The goal is to do this in a unifying framework, namely proof-search in a classical polarized sequent calculus. One of the advantages of this is to combine those techniques more easily. Another one is to envisage extending those techniques.

For instance, the algorithm at the heart of SMT-solving (SAT-modulo-Theory) is DPLL(T), whose theory does not treat existential variables (although SMT-provers often implement incomplete ad hoc techniques for them). We have first encoded DPLL(T) as the step-by-step construction of a proof tree in a classical polarized sequent calculus extended with calls to a decision procedure for T (to be published). This proof-theoretic view now allows us to envisage how to extend the algorithm with existential variables.

Another range of techniques that we are addressing is the handling of equality (superposition / paramodulation calculi).