论文信息 - Negation in bounded commutative DRℓ-monoids

Negation in bounded commutative DRℓ-monoids

The class of commutative dually residuated lattice ordered monoids (DRℓ-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 DRℓ-monoids is introduced, its properties are studied and the sets of regular and dense elements of DRℓ-monoids are described.

Jiří Rachůnek | J. Rachunek | Vladimír Slezák | Vladimír Slezák

[1] K. Swamy,et al. Dually residuated lattice ordered semigroups , 1965 .

[2] Antoni Torrens Torrell,et al. Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic , 2003, Arch. Math. Log..

[3] Jiří Rachůnek,et al. DRl-semigroups and MV-algebras , 1998 .

[4] B. V. Rao,et al. Isometries in Dually Residuated Lattice Ordered Semigroups , 1980 .

[5] D. Mundici,et al. Algebraic Foundations of Many-Valued Reasoning , 1999 .

[6] K. Swamy,et al. Dually Residuated Lattice Ordered Semigroups, II , 1965 .

[7] Jiří Rachůnek. A duality between algebras of basic logic and bounded representable $DRl$-monoids , 2001 .

[8] Petr Hájek,et al. Metamathematics of Fuzzy Logic , 1998, Trends in Logic.