Displaying similar documents to “Interior and Closure Operators on Commutative Bounded Residuated Lattices”

Interior and closure operators on bounded residuated lattices

Jiří Rachůnek, Zdeněk Svoboda (2014)

Open Mathematics

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Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and...

Monotone modal operators on bounded integral residuated lattices

Jiří Rachůnek, Zdeněk Svoboda (2012)

Mathematica Bohemica

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Bounded integral residuated lattices form a large class of algebras containing some classes of commutative and noncommutative algebras behind many-valued and fuzzy logics. In the paper, monotone modal operators (special cases of closure operators) are introduced and studied.

Commutative idempotent residuated lattices

David Stanovský (2007)

Czechoslovak Mathematical Journal

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We investigate the variety of residuated lattices with a commutative and idempotent monoid reduct.

PC-lattices: A Class of Bounded BCK-algebras

Sadegh Khosravi Shoar, Rajab Ali Borzooei, R. Moradian, Atefe Radfar (2018)

Bulletin of the Section of Logic

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In this paper, we define the notion of PC-lattice, as a generalization of finite positive implicative BCK-algebras with condition (S) and bounded commutative BCK-algebras. We investiate some results for Pc-lattices being a new class of BCK-lattices. Specially, we prove that any Boolean lattice is a PC-lattice and we show that if X is a PC-lattice with condition S, then X is an involutory BCK-algebra if and only if X is a commutative BCK-algebra. Finally, we prove that any PC-lattice...

Residuation in orthomodular lattices

Ivan Chajda, Helmut Länger (2017)

Topological Algebra and its Applications

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We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one. ...