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We introduce two unary operators G and H on a relatively pseudocomplemented lattice which form an algebraic axiomatization of the tense quantifiers “it is always going to be the case that” and “it has always been the case that”. Their axiomatization is an extended version for the classical logic and it is in accordance with these operators on many-valued Łukasiewicz logic. Finally, we get a general construction of these tense operators on complete relatively pseudocomplemented lattice which is a...

Algebraic properties of pre-logics

Ivan Chajda, Radomír Halaš (2002)

Mathematica Slovaca

Algebras determined by their endomorphism monoids

V. Koubek, H. Radovanská (1994)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Brouwerian semilattices: The lattice of total subalgebras

Peter Köhler (1982)

Banach Center Publications

Characterization of a full set of probabilities on some posets.

Gill, J.B. (1986)

Publications de l'Institut Mathématique. Nouvelle Série

Characterizations of 0-distributive posets

Vinayak V. Joshi, B. N. Waphare (2005)

Mathematica Bohemica

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

Characterizing triplets for modular pseudocomplemented ordered sets

Ivan Chajda, Radomír Halaš (2000)

Mathematica Slovaca

Complete subobjects of fuzzy sets over $M V$ -algebras

Jiří Močkoř (2004)

Czechoslovak Mathematical Journal

A subobjects structure of the category $Ω$ - of $Ω$ -fuzzy sets over a complete $M V$ -algebra $Ω = (L, \land, \lor, \otimes, \to)$ is investigated, where an $Ω$ -fuzzy set is a pair $𝐀 = (A, δ)$ such that $A$ is a set and $δ A \times A \to Ω$ is a special map. Special subobjects (called complete) of an $Ω$ -fuzzy set $𝐀$ which can be identified with some characteristic morphisms $𝐀 \to Ω^{*} = (L \times L, μ)$ are then investigated. It is proved that some truth-valued morphisms $\neg_{Ω} Ω^{*} \to Ω^{*}, \cap_{Ω}$ , $\cup_{Ω} Ω^{*} \times Ω^{*} \to Ω^{*}$ are characteristic morphisms of complete subobjects.

Congruence kernels of distributive PJP-semilattices

S. N. Begum, Abu Saleh Abdun Noor (2011)

Mathematica Bohemica

A meet semilattice with a partial join operation satisfying certain axioms is a JP-semilattice. A PJP-semilattice is a pseudocomplemented JP-semilattice. In this paper we describe the smallest PJP-congruence containing a kernel ideal as a class. Also we describe the largest PJP-congruence containing a filter as a class. Then we give several characterizations of congruence kernels and cokernels for distributive PJP-semilattices.

Congruence kernels of orthoimplication algebras.

Chajda, I., Halaš, R., Länger, H. (2007)

Acta Mathematica Universitatis Comenianae. New Series

Congruence lattices in varieties with compact intersection property

Filip Krajník, Miroslav Ploščica (2014)

Czechoslovak Mathematical Journal

We say that a variety $𝒱$ of algebras has the Compact Intersection Property (CIP), if the family of compact congruences of every $A \in 𝒱$ is closed under intersection. We investigate the congruence lattices of algebras in locally finite, congruence-distributive CIP varieties and obtain a complete characterization for several types of such varieties. It turns out that our description only depends on subdirectly irreducible algebras in $𝒱$ and embeddings between them. We believe that the strategy used here can...

Congruence pairs for algebras abstracting Kleene and Stone algebras

Rodney Beazer (1985)

Czechoslovak Mathematical Journal

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