A quasi-implication algebra is introduced as an algebraic counterpart of an implication reduct of propositional logic having non-involutory negation (e.g. intuitionistic logic). We show that every pseudocomplemented semilattice induces a quasi-implication algebra (but not conversely). On the other hand, a more general algebra, a so-called pseudocomplemented q-semilattice is introduced and a mutual correspondence between this algebra and a quasi-implication algebra is shown.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1057,
author = {Ivan Chajda and Kamil Du\v sek},
title = {Quasi-implication algebras},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {22},
year = {2002},
pages = {183-198},
zbl = {1028.03050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1057}
}
Ivan Chajda; Kamil Dušek. Quasi-implication algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 22 (2002) pp. 183-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1057/
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