Axioms for a theory of semantic equivalence
Using an uncountable first order language the author considers a propositional fragment of a many-valued logic with min, max, 1-... for conjunction, disjunction and negation, with truth value set the real interval [0,1] and constants for each truth value of [0,1], with an additional two-valued (!) binary predicate for semantic equivalence, with predicate symbols, individual variables and with symbols for modifiers in the sense this notion is used by L. A. Zadeh in connection with linguistic variables. The semantics, in a natural way, is provided by fuzzy sets. The author gives an axiomatization of the set of all true semantic equivalences which he proves to be complete. Unfortunately, only the propositional level is discussed, and only min, max are used for interpreting conjunction and disjunction.
scientific article; zbMATH DE number 4016866