Monadic Bounded Commutative Residuated ℓ-monoids

Bounded commutative residuated ℓ-monoids are a generalization of algebras of propositional logics such as BL-algebras, i.e. algebraic counterparts of the basic fuzzy logic (and hence consequently MV-algebras, i.e. algebras of the Łukasiewicz infinite valued logic) and Heyting algebras, i.e. algebras of the intuitionistic logic. Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. We introduce and study monadic residuated ℓ-monoids as a generalization of monadic MV-algebras.

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