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CBA logic was introduced as a non-associative generalization of the Łukasiewicz many-valued propositional logic. Its algebraic semantic is just the variety of commutative basic algebras. Petr Hájek introduced vt-operators as models for the “very true” connective on fuzzy logics. The aim of the paper is to show possibilities of using vt-operators on commutative basic algebras, especially we show that...
Hájek introduced the logic $$BL_{vt}$$ enriching the logic BL by a unary connective vt which is a formalization of Zadeh’s fuzzy truth value “very true”. $$\hbox{BL}_{vt}$$ algebras, i.e., BL-algebras with unary operations, called vt-operators, which are among others subdiagonal, are an algebraic counterpart of $$BL_{vt}.$$ Partially ordered commutative integral residuated monoids (pocrims)...
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