Section: Application Domains

Automated Reasoning

Automated reasoning has traditionally focused on classical first-order logic but it is increasingly important for automation to other logics. We are applying our research to the following extensions to this traditional focus.

• Non-classical logics are increasingly becoming important in the specification and analysis of software. Most type systems are based on (possibly second-order) propositional intuitionistic logic, for example, while resource-sensitive and concurrent systems are most naturally expressed in linear logic. The members of the Parsifal team have a strong expertise in the design and implementation of performant automated reasoning systems for such non-classical logics. In particular, the Linprover suite of provers  [38] continue to be the fastest automated theorem provers for propositional and first-order linear logic.

• 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 focused logic. One of the advantages of this approach is that it allows combining and extending such techniques. For example, the PSI project has applied this approach to proof to the problem of SAT-modulo-Theory. In that domain, logical reasoning is combined with domain-specific decision procedures. The PSI project has shown how to incorporate the call to decision procedures in the proof-theoretical framework of focused sequent calculi and the proof-search mechanisms that are related to it.