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On a periodic part of pseudo-BCI-algebras

100%
Dymek G.
Discussiones Mathematicae - General Algebra and Applications
|
2015
|
tom 35
|
nr 2
139-157
EN
In the paper the connections between the set of some maximal elements of a pseudo-BCI-algebra and deductive systems are established. Using these facts, a periodic part of a pseudo-BCI-algebra is studied.
2
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Some properties of pseudo-BCI algebras

100%
Dymek G.
Commentationes Mathematicae
|
2018
|
tom 58
|
nr 1-2
EN
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.
3
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Distributive implication groupoids

88%
Chajda I., Halaš R.
Open Mathematics
|
2007
|
tom 5
|
nr 3
484-492
EN
We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.
4
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On the Leibniz congruences

63%
Font J. M.
Banach Center Publications
|
1993
|
tom 28
|
nr 1
17-36
EN
The aim of this paper is to discuss the motivation for a new general algebraic semantics for deductive systems, to introduce it, and to present an outline of its main features. Some tools from the theory of abstract logics are also introduced, and two classifications of deductive systems are analysed: one is based on the behaviour of the Leibniz congruence (the maximum congruence of a logical matrix) and the other on the behaviour of the Frege operator (which associates to every theory the interderivability relation modulo the theory). For protoalgebraic deductive systems the class of algebras associated in general turns out to be the class of algebra reducts of reduced matrices, which is the algebraic counterpart usually considered for this large class of deductive systems; but in the general case the new class of algebras shows a better behaviour.
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