In this paper we investigate a propositional fuzzy logical system LΠ which contains the well-known Lukasiewicz, Product and Gödel fuzzy logics as sublogics. We define the corresponding algebraic structures, called LΠ-algebras and prove the following completeness result: a formula φ is provable in the LΠ logic iff it is a tautology for all linear LΠ-algebras. Moreover, linear LΠ-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law.
@article{urn:eudml:doc:39172,
title = {Putting together Lukasiewicz and product logics.},
journal = {Mathware and Soft Computing},
volume = {6},
year = {1999},
pages = {219-234},
zbl = {0953.03030},
mrnumber = {MR1774568},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39172}
}
Esteva, Francesc; Godo, Lluis. Putting together Lukasiewicz and product logics.. Mathware and Soft Computing, Tome 6 (1999) pp. 219-234. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39172/