Putting together Lukasiewicz and product logics.

Esteva, Francesc, and Godo, Lluis. "Putting together Lukasiewicz and product logics.." Mathware and Soft Computing 6.2-3 (1999): 219-234. <http://eudml.org/doc/39172>.

@article{Esteva1999,
abstract = {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.},
author = {Esteva, Francesc, Godo, Lluis},
journal = {Mathware and Soft Computing},
keywords = {Lógica difusa; Algebras difusas; Lukasiewicz logic; product logic},
language = {eng},
number = {2-3},
pages = {219-234},
title = {Putting together Lukasiewicz and product logics.},
url = {http://eudml.org/doc/39172},
volume = {6},
year = {1999},
}

TY - JOUR
AU - Esteva, Francesc
AU - Godo, Lluis
TI - Putting together Lukasiewicz and product logics.
JO - Mathware and Soft Computing
PY - 1999
VL - 6
IS - 2-3
SP - 219
EP - 234
AB - 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.
LA - eng
KW - Lógica difusa; Algebras difusas; Lukasiewicz logic; product logic
UR - http://eudml.org/doc/39172
ER -