# A glimpse of deductive systems in algebra

Open Mathematics (2010)

• Volume: 8, Issue: 4, page 688-705
• ISSN: 2391-5455

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## Abstract

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The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.

## How to cite

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Dumitru Buşneag, and Sergiu Rudeanu. "A glimpse of deductive systems in algebra." Open Mathematics 8.4 (2010): 688-705. <http://eudml.org/doc/269026>.

@article{DumitruBuşneag2010,
abstract = {The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.},
author = {Dumitru Buşneag, Sergiu Rudeanu},
journal = {Open Mathematics},
keywords = {Deductive system; Filter; ⊙-filter; Strong filter; Algebra of logic; Hilbert algebra; pre-BCK algebra; deductive system; filter; strong filter; algebra of logic},
language = {eng},
number = {4},
pages = {688-705},
title = {A glimpse of deductive systems in algebra},
url = {http://eudml.org/doc/269026},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Dumitru Buşneag
AU - Sergiu Rudeanu
TI - A glimpse of deductive systems in algebra
JO - Open Mathematics
PY - 2010
VL - 8
IS - 4
SP - 688
EP - 705
AB - The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras.
LA - eng
KW - Deductive system; Filter; ⊙-filter; Strong filter; Algebra of logic; Hilbert algebra; pre-BCK algebra; deductive system; filter; strong filter; algebra of logic
UR - http://eudml.org/doc/269026
ER -

## References

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