Page 1 Next

Displaying 1 – 20 of 21

Showing per page

IF-filters of pseudo-BL-algebras

Magdalena Wojciechowska-Rysiawa (2015)

Discussiones Mathematicae - General Algebra and Applications

Characterizations of IF-filters of a pseudo-BL-algebra are established. Some related properties are investigated. The notation of prime IF- filters and a characterization of a pseudo-BL-chain are given. Homomorphisms of IF-filters and direct product of IF-filters are studied.

Implication algebras

Ivan Chajda (2006)

Discussiones Mathematicae - General Algebra and Applications

We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unified approach enables us to compare the mentioned algebras and apply a unified treatment of congruence properties....

Implication and equivalential reducts of basic algebras

Ivan Chajda, Miroslav Kolařík, Filip Švrček (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A term operation implication is introduced in a given basic algebra and properties of the implication reduct of are treated. We characterize such implication basic algebras and get congruence properties of the variety of these algebras. A term operation equivalence is introduced later and properties of this operation are described. It is shown how this operation is related with the induced partial order of and, if this partial order is linear, the algebra can be reconstructed by means of...

Implicative hyper -algebras

Mohammad Mehdi Zahedi, A. Borumand Saeid, R. A. Borzooei (2005)

Czechoslovak Mathematical Journal

In this note we first define the notions of (weak, strong) implicative hyper -algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper -ideals. Also we obtain some relations between these notions and (weak) implicative hyper -ideals. Finally, we study the implicative hyper -algebras of order 3, in particular we obtain a relationship between the positive implicative...

Incomparable families and maximal trees

G. Campero-Arena, J. Cancino, M. Hrušák, F. E. Miranda-Perea (2016)

Fundamenta Mathematicae

We answer several questions of D. Monk by showing that every maximal family of pairwise incomparable elements of 𝒫(ω)/fin has size continuum, while it is consistent with the negation of the Continuum Hypothesis that there are maximal subtrees of both 𝒫(ω) and 𝒫(ω)/fin of size ω₁.

Interior and closure operators on bounded commutative residuated l-monoids

Jiří Rachůnek, Filip Švrček (2008)

Discussiones Mathematicae - General Algebra and Applications

Topological Boolean algebras are generalizations of topological spaces defined by means of topological closure and interior operators, respectively. The authors in [14] generalized topological Boolean algebras to closure and interior operators of MV-algebras which are an algebraic counterpart of the Łukasiewicz infinite valued logic. In the paper, these kinds of operators are extended (and investigated) to the wide class of bounded commutative Rl-monoids that contains e.g. the classes of BL-algebras...

Interior and closure operators on bounded residuated lattices

Jiří Rachůnek, Zdeněk Svoboda (2014)

Open Mathematics

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 on the residuated...

Interior and closure operators on bounded residuated lattice ordered monoids

Filip Švrček (2008)

Czechoslovak Mathematical Journal

-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior -algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on -monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on -algebras.

Interior and Closure Operators on Commutative Bounded Residuated Lattices

Jiří Rachůnek, Zdeněk Svoboda (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Commutative 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 additive closure and multiplicative interior operators on this class of algebras.

Interrelation of algebraic, semantical and logical properties for superintuitionistic and modal logics

Larisa Maksimova (1999)

Banach Center Publications

We consider the families 𝓛 of propositional superintuitionistic logics (s.i.l.) and NE(K) of normal modal logics (n.m.l.). It is well known that there is a duality between 𝓛 and the lattice of varieties of pseudo-boolean algebras (or Heyting algebras), and also NE(K) is dually isomorphic to the lattice of varieties of modal algebras. Many important properties of logics, for instance, Craig's interpolation property (CIP), the disjunction property (DP), the Beth property (BP), Hallden-completeness...

Currently displaying 1 – 20 of 21

Page 1 Next