Displaying similar documents to “A duality between algebras of basic logic and bounded representable D R l -monoids”

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.

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...

Weak Boolean products of bounded dually residuated l -monoids

Jan Kühr, Jiří Rachůnek (2007)

Mathematica Bohemica

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In the paper we deal with weak Boolean products of bounded dually residuated ℓ -monoids (DRl-monoids). Since bounded DRl-monoids are a generalization of pseudo MV-algebras and pseudo BL-algebras, the results can be immediately applied to these algebras.