Gödel Homomorphisms as Gödel Modal Operators

Issue title: MFCS & CSL 2010 Satellite Workshops: Selected Papers

Article type: Research Article

Authors: Fasching, Oliver

Affiliations: Gudrunstrasse 5/1/15, 1110 Vienna, Austria. [email protected]

Note: [] supported by the Austrian Science Fund (FWF): P22416 Address for correspondence: Gudrunstrasse 5/1/15, 1110 Vienna, Austria

Abstract: We extend propositional Gödel logic by a unary modal operator, which we interpret as Gödel homomorphisms, i.e. functions [0, 1] → [0, 1] that distribute over the interpretations of the binary connectives of Gödel logic. We show weak completeness of the propositional fragment w.r.t. a simple superintuitionistic Hilbert-type proof system, and we prove that validity does not change if we use the function class of continuous, strictly increasing functions. We also give proof systems for restrictions to sub- and superdiagonal functions.

Keywords: Gödel logic, superintuitionistic logic, modal logic, truth stressers

DOI: 10.3233/FI-2013-799

Journal: Fundamenta Informaticae, vol. 123, no. 1, pp. 43-57, 2013