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Algebraic axiomatization of tense intuitionistic logic

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Chajda I.

Open Mathematics

2011

tom 9

nr 5

1185-1191

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.

Interior and closure operators on bounded residuated lattices

100%

Rachůnek J., Svoboda Z.

Open Mathematics

2014

tom 12

nr 3

534-544

Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and on the residuated lattices of their regular elements.

Ograniczanie wyników

2 Open Mathematics

1 Chajda I.

1 Rachůnek J.

1 Svoboda Z.

1 2014

1 2011

Wyniki wyszukiwania

Algebraic axiomatization of tense intuitionistic logic

Interior and closure operators on bounded residuated lattices