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Some properties of pseudo-BCI algebras

Dymek G.

Commentationes Mathematicae

2018

Vol. 58, No. 1/2

19--35

In this paper the notion of an essential closed deductive system of a pseudo-BCI algebra is defined and investigated. Among other things, it is proved that such a deductive system contains all coatoms of the pseudo-BCI algebra. Also, the notions of homomorphisms and semihomomorphisms of pseudo-BCI algebras are studied and some of their properties are presented.

Pseudo BCK-semilattices

Kuhr J.

Demonstratio Mathematica

2007

Vol. 40, nr 3

495-516

Pseudo BCK-algebras are algebras (A,approaches 1) of type (2, 2, 0) which generalize BCK-algebras in such a way that if the operations-› and ->coincide then (A,-›, 1) is a BCK-algebra. They can be also viewed as {-›,->, 1}-subreducts of non-commutative integral residuated lattices. In the paper, we study pseudo BCK-algebras whose underlying posets are semilattices or lattices; we call them pseudo BCK-join-semilattices, pseudo BCK-meet-semilattices and pseudo BCK-lattices, respectively. After describing their congruence properties we deal mainly with prime deductive systems of pseudo BCK-join-semilattices.

A Strong Completeness Result for a MAS Logic

Kacprzak M.

Fundamenta Informaticae

2006

Vol. 72, nr 1-3

197-213

The paper introduces an original formalization of distributed systems which work in a concurrent way, especially multi-agent systems (MAS). The described deductive system, called RA-MAS, is based on elements of branching time temporal logic, epistemic logic and algorithmic logic. The established operators and modalities allow to compare different multi-agent systems on the basis of the same formal system. Moreover, the logic provides tools for modelling and characterizing mental features of agents as well as different forms of cooperation. The main aim of the paper is to present axiomatization and prove a strong completeness result for the logic. The proof is inspired by a combination of the algebraic method of Rasiowa and Sikorski for classical logic with the Kripke method for modal logic.