Displaying similar documents to “Modal operators on bounded commutative residuated ℓ -monoids”

Modal operators on bounded residuated l -monoids

Jiří Rachůnek, Dana Šalounová (2008)

Mathematica Bohemica

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Bounded residuated lattice ordered monoids ( R ℓ -monoids) form a class of algebras which contains the class of Heyting algebras, i.e. algebras of the propositional intuitionistic logic, as well as the classes of algebras of important propositional fuzzy logics such as pseudo MV -algebras (or, equivalently, GMV -algebras) and pseudo BL -algebras (and so, particularly, MV -algebras and BL -algebras). Modal operators on Heyting algebras were studied by Macnab (1981), on MV -algebras were studied by Harlenderová...

Negation in bounded commutative D R ℓ -monoids

Jiří Rachůnek, Vladimír Slezák (2006)

Czechoslovak Mathematical Journal

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The class of commutative dually residuated lattice ordered monoids ( D R ℓ -monoids) contains among others Abelian lattice ordered groups, algebras of Hájek’s Basic fuzzy logic and Brouwerian algebras. In the paper, a unary operation of negation in bounded D R ℓ -monoids is introduced, its properties are studied and the sets of regular and dense elements of D R ℓ -monoids are described.

A duality between algebras of basic logic and bounded representable D R l -monoids

Jiří Rachůnek (2001)

Mathematica Bohemica

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B L -algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that B L -algebras are the duals of bounded representable D R l -monoids. This duality enables us to describe some structure properties of B L -algebras.