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Putting together Lukasiewicz and product logics

Other TitlesJuntando las lógicas de Lukasiewicz y producto
AuthorsEsteva, Francesc CSIC ORCID ; Godo, Lluis CSIC ORCID
KeywordsFuzzy logics
Fuzzy algebras
Issue Date1999
PublisherUniversidad Politécnica de Cataluña
CitationMathware and Soft Computing, 1999, 6 (2-3): 219-234.
AbstractIn 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.
DescriptionThis is a revised version of the paper with the same title appeared in the Proc. of the Estylf'98 Conference, September 8-10, 1998, Pamplona (Spain).
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