The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.
@article{bwmeta1.element.bwnjournal-article-bcpv28z1p51bwm,
author = {Pigozzi, Don and Salibra, Antonino},
title = {Polyadic algebras over nonclassical logics},
journal = {Banach Center Publications},
volume = {28},
year = {1993},
pages = {51-66},
zbl = {0794.03092},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv28z1p51bwm}
}
Pigozzi, Don; Salibra, Antonino. Polyadic algebras over nonclassical logics. Banach Center Publications, Tome 28 (1993) pp. 51-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv28z1p51bwm/
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