Proof-search and countermodel generation for non-normal modal logics: The theorem prover PRONOM-Reference-Cited by-同舟云学术

Proof-search and countermodel generation for non-normal modal logics: The theorem prover PRONOM

Published:2021-01-11 Issue:2 Volume:14 Page:215-229
ISSN:1724-8035
Container-title:Intelligenza Artificiale
language:
Short-container-title:IA

Author:

Dalmonte Tiziano¹^ORCID,Negri Sara²³^ORCID,Olivetti Nicola¹^ORCID,Pozzato Gian Luca⁴^ORCID

Affiliation:

1. Aix-Marseille University, Université de Toulon, CNRS, Marseille Cedex, France

2. Department of Philosophy, University of Helsinki, Helsinki, Finland

3. Dipartimento di Matematica, Università di Genova, Genova, Italy

4. Dipartimento di Informatica, Università di Torino, Torino, Italy

Abstract

In this work 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 a sequent with an empty left-hand side and containing only that formula on the right-hand side as a root, 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.

Publisher

IOS Press

Subject

Artificial Intelligence

Reference23 articles.

1. CSLlean: A theorem-prover for the logic of comparative concept similarity;Alenda;Electronic Notes in Theoretical Computer Science (ENTCS),2010

2. Knowledge means ‘all’, belief means ‘most’;Askounis;Journal of Applied Non-Classical Logics,2016

3. Modal Logic

4. Dalmonte T. , Negri S. , Olivetti N. , Pozzato. G.L. . PRONOM: proof-search and countermodel generation for non-normal modal logics. In Mario Alviano, Gianluigi Greco, and Francesco Scarcello, editors, AI*IA 2019 – Advances in Artificial Intelligence - XVIIIth International Conference of the Italian Association for Artificial Intelligence, Rende, Italy, November 19-22, 2019, Proceedings, volume 11946 of Lecture Notes in Computer Science, pages 165–179. Springer, (2019).

5. Dalmonte T. , Olivetti N. , Negri. S. . Nonnormal modal logics: Bi-neighbourhood semantics and its labelled calculi, In Guram Bezhanishvili, Giovanna D’Agostino, George Metcalfe, and Thomas Studer, editors, Advances in Modal Logic 12, proceedings of the 12th conference on Advances in Modal Logic, held in Bern, Switzerland, August 27–31, 2018, pages 159–178. College Publications, (2018).