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Algebra Logika, 2006 Volume 45, Number 6, Pages 731–757 (Mi al167)
This article is cited in 1 paper

Fuzzy logics with modalities

O. V. Zeeval'd

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We explore the basic fuzzy logic $BL$ as well as propositional fuzzy logics with modalities $\Box$ and $\diamond$ and a total accessibility relation. Formulations and proofs are given to replacement theorems for $BL$. A basic calculus of modal fuzzy logic is introduced. For this calculus and its extensions, we prove replacement and deduction theorems.

Keywords: basic fuzzy logic, $BL$-algebra, modality, Kripke $L$-structure, calculus, schematic extension, replacement theorem, deduction theorem.

UDC: 510.64

Received: 03.03.2006


 English version: Algebra and Logic, 2006, 45:6, 415–430

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© Steklov Math. Inst. of RAS, 2024