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Quantum B-algebras

Wolfgang Rump (2013)

Open Mathematics

The concept of quantale was created in 1984 to develop a framework for non-commutative spaces and quantum mechanics with a view toward non-commutative logic. The logic of quantales and its algebraic semantics manifests itself in a class of partially ordered algebras with a pair of implicational operations recently introduced as quantum B-algebras. Implicational algebras like pseudo-effect algebras, generalized BL- or MV-algebras, partially ordered groups, pseudo-BCK algebras, residuated posets,...

Quantum logics and bivariable functions

Eva Drobná, Oľga Nánásiová, Ľubica Valášková (2010)

Kybernetika

New approach to characterization of orthomodular lattices by means of special types of bivariable functions G is suggested. Under special marginal conditions a bivariable function G can operate as, for example, infimum measure, supremum measure or symmetric difference measure for two elements of an orthomodular lattice.

Quasi-implication algebras

Ivan Chajda, Kamil Dušek (2002)

Discussiones Mathematicae - General Algebra and Applications

A quasi-implication algebra is introduced as an algebraic counterpart of an implication reduct of propositional logic having non-involutory negation (e.g. intuitionistic logic). We show that every pseudocomplemented semilattice induces a quasi-implication algebra (but not conversely). On the other hand, a more general algebra, a so-called pseudocomplemented q-semilattice is introduced and a mutual correspondence between this algebra and a quasi-implication algebra is shown.

Quasi-modal algebras

Sergio A. Celani (2001)

Mathematica Bohemica

In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.

Quotient hyper pseudo BCK-algebras

Habib Harizavi, Tayebeh Koochakpoor, Rajab Ali Boorzoei (2013)

Discussiones Mathematicae - General Algebra and Applications

In this paper, we first investigate some properties of the hyper pseudo BCK-algebras. Then we define the concepts of strong and reflexive hyper pseudo BCK-ideals and establish some relationships among them and the other types of hyper pseudo BCK-ideals. Also, we introduce the notion of regular congruence relation on hyper pseudo BCK-algebras and investigate some related properties. By using this relation, we construct the quotient hyper pseudo BCK-algebra and give some related results.

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