Theorem Proving for Non-normal Modal Logics

Tiziano Dalmonte (1, 2) , Sara Negri (3, 4) , Nicola Olivetti (1, 2) , Gian Luca Pozzato (5)

1 LIRICA - Logique, Interaction, Raisonnement et Inférence, Complexité, Algèbre
2 AMU - Aix Marseille Université
3 Helsingin yliopisto = Helsingfors universitet = University of Helsinki
4 UniGe - Università degli studi di Genova = University of Genoa
5 UNITO - Università degli studi di Torino = University of Turin

In this work we briefly summarize our recent contributions in the field of proof methods, theorem proving and countermodel generation for non-normal modal logics. We first recall some labelled sequent calculi for the basic system E and its extensions with axioms M, N, and C based on bi-neighbourhood semantics. Then, we present PRONOM, a theorem prover and countermodel generator for non-normal modal logics implemented in Prolog. When a modal formula is valid, then PRONOM computes a proof in the labelled calculi, otherwise it is able to extract a model falsifying it from an open, saturated branch.

Domaines: Logique en informatique [cs.LO]

Tiziano Dalmonte, Sara Negri, Nicola Olivetti, Gian Luca Pozzato. Theorem Proving for Non-normal Modal Logics. OVERLAY 2020, Sep 2021, Udine, Italy. ⟨hal-03159954⟩