Putting together Lukasiewicz and product logics
Putting together Lukasiewicz and product logics
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.
The authors acknowledge partial support of this work through CICYT Project SMASH (TIC96-1138-C04-01/04) and of the COST Action 15 of the European Union.
This 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).
Peer reviewed
Ordered rings, algebras, modules, Classificació AMS::03 Mathematical logic and foundations::03B General logic, Fuzzy logics, Fuzzy logic; logic of vagueness, Other algebras related to logic, Fuzzy logic, product logic, Lògica matemàtica, Lukasiewicz logic, :03 Mathematical logic and foundations::03B General logic [Classificació AMS], Many-valued logic, Ł∏ algebras, Fuzzy algebras
Ordered rings, algebras, modules, Classificació AMS::03 Mathematical logic and foundations::03B General logic, Fuzzy logics, Fuzzy logic; logic of vagueness, Other algebras related to logic, Fuzzy logic, product logic, Lògica matemàtica, Lukasiewicz logic, :03 Mathematical logic and foundations::03B General logic [Classificació AMS], Many-valued logic, Ł∏ algebras, Fuzzy algebras
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