On very true operators on pocrims
Hjek introduced the logic \(BL_{vt}\) enriching the logic BL by a unary connective vt which is a formalization of Zadehs 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) are common generalizations of both BL-algebras and Heyting algebras. The aim of our paper is to introduce and study algebraic properties of pocrims endowed by very-true and very-false-like operators.
pocrim bl-algebra vt-operator wvt-operator mv-algebra