ABSTRACT. Bounded commutative residuated lattice ordered monoids (R -monoids) are a common generalization of, e.g., Heyting algebras and BL-algebras, i.e., algebras of intuitionistic logic and basic fuzzy logic, respectively. , also algebras of logics behind fuzzy reasoning can be considered as particular cases of bounded commutative R -monoids. Namely from this point of view, M V -algebras, an algebraic counterpart of the Lukasiewicz infinitevalued propositional logic, are precisely bounded commutative R -monoids satisfying the double negation law. Further, BL-algebras, an algebraic semantics of the Há j e k basic fuzzy logic, are just bounded commutative R -monoids isomorphic to subdirect products of linearly ordered commutative R -monoids. Heyting algebras (duals to Brouwerian algebras), i.e. algebras of intuitionistic logic, are characterized as bounded commutative R -monoids with idempotent multiplication.2000 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: Primary 06D35, 06F05. K e y w o r d s: residuated -monoid, residuated lattice, BL-algebra, MV -algebra.
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