PRONOM: proof-search and countermodel generation for non-normal modal logics

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

1 LIRICA - Logique, Interaction, Raisonnement et Inférence, Complexité, Algèbre
2 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
3 Helsingin yliopisto = Helsingfors universitet = University of Helsinki
4 UNITO - Università degli studi di Torino = University of Turin

We present PRONOM, a theorem prover and countermodel generator for non-normal modal logics. PRONOM implements some labelled sequent calculi recently introduced for the basic system E and its extensions with axioms M, N, and C based on bi-neighbourhood semantics. PRONOM is inspired by the methodology of leanTAP and is implemented in Prolog. When a modal formula is valid, then PRONOM computes a proof (a closed tree) in the labelled calculi having that formula as a root in the labelled calculi, otherwise PRONOM is able to extract a model falsifying it from an open, saturated branch. The paper shows some experimental results, witnessing that the performances of PRONOM are promising.

Domaines: Logique en informatique [cs.LO]; Intelligence artificielle [cs.AI]

Tiziano Dalmonte, Sara Negri, Nicola Olivetti, Gian Luca Pozzato. PRONOM: proof-search and countermodel generation for non-normal modal logics. AIIA 2019: 18th International Conference of the Italian Association for Artificial Intelligence, Nov 2019, Rende, Italy. ⟨hal-02439537⟩