Decidability for S4 Gödel Modal Logics

Authors: M. Diéguez, David Fernández-Duque
Publication year: 2023
Publication type: Kapitola v monografii
Periodical: Computational Intelligence and Mathematics for Tackling Complex Problems 4
Projects: Metamathematics of substructural modal logics
Bibliographic citation: DIÉGUEZ, M., FERNÁNDEZ-DUQUE, David. Decidability for S4 Gödel Modal Logics. In: CORNEJO, M. E., HARMATI, I. A., KOCZY, L. T., MEDINA-MORENO, J., eds. Computational Intelligence and Mathematics for Tackling Complex Problems 4. Cham: Springer, 2023, S. 1-7. Studies in Computational Intelligence, 1040. ISBN 978-3-031-07706-7
Dostupné z: doi:10.1007/978-3-031-07707-4_1.
DOI: 10.1007/978-3-031-07707-4_1
ID: 563809
Online record: View online record

Abstract

We introduce semantics for crisp and fuzzy Gödel S4 based on bi-relational frames. We then show that each version of the logic is sound and complete for its respective class of frames and enjoys the finite model property. From this we conclude that both the crisp and fuzzy versions of Gödel S4 are decidable.