## Section: Application Domains

### Automated reasoning and SMT solving

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 polarized and focussed logic. One of the advantages of this is to combine those techniques more easily. Another one is to envisage extending those techniques.

For instance, SAT-modulo-Theory problems require the combination of logical reasoning with domain-specific decision procedures. So in the PSI project we study how to incorporate the call to decision procedures in proof-theoretical framework like the focussed sequent calculus, and the proof-search mechanisms that are related to it.

In the same spirit we also study how to handle existential variables and equality, for which specific automated reasoning techniques have been designed (superposition / paramodulation calculi).