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Keywords:
residuated $\text{\rm l}$-monoid; non-classical logics; basic fuzzy logic; intuitionistic logic; filter; fuzzy filter; $\text{\rm BL}$-algebra; $\text{\rm MV}$-algebra; Heyting algebra
Summary:
The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (\rl monoids) are common generalizations of $\text{\rm BL}$-algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters of the corresponding algebras. In the paper we investigate implicative, positive implicative, Boolean and fantastic fuzzy filters of bounded $\text{\rm Rl}$-monoids.
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