State BCK-algebras and State-Morphism BCK-algebras

In the paper, we define the notion of a state BCK-algebra and a state-morphism BCK-algebra extending the language of BCK-algebras by adding a unary operator which models probabilistic reasoning. We present a relation between state operators and state-morphism operators and measures and states on BCK...

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Bibliographic Details
Main Authors Borzooei, R. A, Dvurečenskij, A, Zahiri, O
Format Journal Article
LanguageEnglish
Published 25.04.2013
Subjects
Mathematics - Commutative Algebra
Mathematics - Rings and Algebras
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Summary:In the paper, we define the notion of a state BCK-algebra and a state-morphism BCK-algebra extending the language of BCK-algebras by adding a unary operator which models probabilistic reasoning. We present a relation between state operators and state-morphism operators and measures and states on BCK-algebras, respectively. We study subdirectly irreducible state (morphism) BCK-algebras. We introduce the concept of an adjoint pair in BCK-algebras and show that there is a one-to-one correspondence between adjoint pairs and state-morphism operators. In addition, we show the generators of quasivarieties of state-morphism BCK-algebras.
DOI:10.48550/arxiv.1304.6963