Work

Intuitionistic S4 is decidable

Year: 2023

Type: conference-paper

Abstract: In this paper we demonstrate decidability for the intuitionistic modal logic S4 first formulated by Fischer Servi. This solves a problem that has been open for almost thirty years since it had been posed in Simpson’s PhD thesis in 1994. We obtain this result by performing proof search in a labelled deductive system that, instead of using only one binary relation on the labels, employs two: one corresponding to the accessibility relation of modal logic and the other corresponding to the order relation of intuitionistic Kripke frames. Our search algorithm outputs either a proof or a finite counter-model, thus, additionally establishing the finite model property for intuitionistic S4, which has been another long-standing open problem in the area.

Source: Proceedings - Symposium on Logic in Computer Science

DOI: 10.1109/lics56636.2023.10175684

Authors: Marianna Girlando, Roman Kuznets, Sonia Marin, Marianela Morales, Lutz Straßburger

Institutions: University of Birmingham, University of Amsterdam, TU Wien, Centre Inria de Saclay

Language: English

Topic: Logic, Reasoning, and Knowledge

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Austrian Science Fund, HORIZON EUROPE Marie Sklodowska-Curie Actions

Award: CYclic DErivations for Recursive operators