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Algebraic axiomatization of tense intuitionistic logic

100%
Chajda I.
Open Mathematics
|
2011
|
tom 9
|
nr 5
1185-1191
EN
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 power lattice via the so-called frame.
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A glimpse of deductive systems in algebra

81%
Buşneag D., Rudeanu S.
Open Mathematics
|
2010
|
tom 8
|
nr 4
688-705
EN
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.
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