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On modal extensions of product fuzzy logic. (English) Zbl 1390.03025

Authors’ abstract: In this article, we study modal extensions of product fuzzy logic with both algebraic semantics and relational semantics based on Kripke structures with crisp accessibility relations, when the underlying product fuzzy logic is expanded with truth-constants, the \(\Delta\) operator and with two infinitary inference rules. We provide completeness results for both kinds of semantics. Finally, we also consider a generalization of possibilistic logic evaluated over product algebras.

MSC:

03B52 Fuzzy logic; logic of vagueness
03B45 Modal logic (including the logic of norms)
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