An Algebraic Study of S5-Modal Gödel Logic

In this paper we continue the study of the variety MG of monadic Gödel algebras. These algebras are the equivalent algebraic semantics of the S5-modal expansion of Gödel logic, which is equivalent to the one-variable monadic fragment of first-order Gödel logic. We show three families of locally fini...

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Bibliographic Details
Published in:Studia logica 2021-10, Vol.109 (5), p.937-967
Main Authors: Castaño, Diego, Cimadamore, Cecilia, Varela, José P. Díaz, Rueda, Laura
Format: Article
Language:English
Subjects:
Computational Linguistics
Education
Logic
Mathematical Logic and Foundations
Philosophy
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Summary:In this paper we continue the study of the variety MG of monadic Gödel algebras. These algebras are the equivalent algebraic semantics of the S5-modal expansion of Gödel logic, which is equivalent to the one-variable monadic fragment of first-order Gödel logic. We show three families of locally finite subvarieties of MG and give their equational bases. We also introduce a topological duality for monadic Gödel algebras and, as an application of this representation theorem, we characterize congruences and give characterizations of the locally finite subvarieties mentioned above by means of their dual spaces. Finally, we study some further properties of the subvariety generated by monadic Gödel chains: we present a characteristic chain for this variety, we prove that a Glivenko-type theorem holds for these algebras and we characterize free algebras over n generators.
ISSN:0039-3215
1572-8730
DOI:10.1007/s11225-020-09934-x