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Algebraic and proof-theoretic characterizations of truth stressers for MTL and its extensions. (English) Zbl 1190.03026
Truth stressers, also known as modifiers in approximate reasoning applications of fuzzy logics, are modeled here as a kind of modalities. This generalizes an idea offered by P. Hájek [Fuzzy Sets Syst. 124, No. 3, 329–333 (2001; Zbl 0997.03028)] for the particular truth stresser “very true”.
The authors extend the Hilbert-type calculus of monoidal t-norm logic MTL, as well as of suitable related mathematical fuzzy logics, with such operators, develop adequate algebraic semantics (the truth stressers correspond to kinds of interior operators in residuated lattices) and give also equivalent hypersequent calculi. And they get decidability results via the discussion of the finite embeddability property.

MSC:
03B52 Fuzzy logic; logic of vagueness
03B45 Modal logic (including the logic of norms)
03B50 Many-valued logic
03F52 Proof-theoretic aspects of linear logic and other substructural logics
03G25 Other algebras related to logic
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