Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Fuzzy logic and arithmetical hierarchy
Fuzzy Sets and Systems
A geometric proof of the completeness of the Lukasiewicz calculus
Journal of Symbolic Logic
An invitation to Chang's MV algebras
Selected surveys presented at two conferences on Advances in algebra and model theory
On a class of residuated semilattice monoids
Fuzzy Sets and Systems
A logic for reasoning about the probability of fuzzy events
Fuzzy Sets and Systems
On triangular norms and uninorms definable in Ł Π12
International Journal of Approximate Reasoning
Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
Barycentric Algebras and Gene Expression
WILF '09 Proceedings of the 8th International Workshop on Fuzzy Logic and Applications
Implicit operations in MV-algebras and the connectives of Łukasiewicz logic
Algebraic and proof-theoretic aspects of non-classical logics
Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
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We investigate the variety corresponding to a logic (introduced in Esteva and Godo, 1998, and called ŁΠ there),which is the combination of Łukasiewicz Logic and ProductLogic, and in which Gödel Logic is interpretable. We present an alternative (and slightly simpler) axiomatization of such variety. We also investigate the variety, called the variety of ŁΠ½ algebras, corresponding to the logic obtained from ŁΠ by the adding of a constant and of a defining axiom for one half.We also connect ŁΠ½ algebras with structures, called f-semifields, arising from the theory oflattice-ordered rings, and prove that every ŁΠ½ algebra \cal A can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield \cal F, and whoseoperations are the truncations of the operations of \cal F to [0, 1]. We prove that such a structure \cal Fis uniquely determined by \cal A up to isomorphism, and we establish an equivalence between the category of ŁΠ½ algebras and that of f-semifields.