Abstract
This chapter summarizes the properties of the model theory of fuzzy logic in narrow sense with evaluated syntax (FLn), based on the set of truth-values that forms the Lukasiewicz MV-algebra. FLn with evaluated syntax possesses several properties that are generalizations of the corresponding properties of classical logic, their proofs are mostly non-trivial and complex. The main results concern elementary extensions and elementary chains. Besides other outcomes, they enable to see classical logic from different point of view. The concepts of submodel (substructure), elementary submodel, elementary equivalence, homomorphis, and isomorphism of models are already defined in the chapter. Several special properties that have no counterpart in classical logic are also introduced. This concerns various kinds of relations among models of fuzzy theoriesthat can be generalized to hold in some general degree only. Such generalization can be useful in areas such as modeling of natural language semantics or theories dealing with prototypes.
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