Gödel logics with monotone operators

Authors:
Matthias Baaz;Oliver Fasching
Affiliations:
Vienna University of Technology, Wiedner Hauptstraße 8--10/E104.2, 1040 Wien, Austria;Vienna University of Technology, Wiedner Hauptstraße 8--10/E104.2, 1040 Wien, Austria
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

We consider the extension of Godel logic by a unary operator interpreted by functions on the unit interval with certain monotonicity properties. We prove that validity of propositional formulas is decidable by giving a sound and complete proof system with finitely many axioms. We show also how to transfer the deduction theorem, the lifting lemma and the agreement of entailment and 1-entailment from Godel logic to the propositional fragment of our extension. Finally, we prove an enumerability result for a ring-normal prenex fragment.