Some model theory in fuzzy logic

Petr Hájek

Czech Academy of Sciences, Prague

A model-theoretic characterization of conservative extensions of axiomatic theories over the basic fuzzy predicate logic BL will be presented. Furthermore, the notion of witnessed models will be discussed, a model being witnessed if for each quantified formula its truth value in the model (defined as the supremum/infimum of values of instances) is in fact maximum/supremum. A completeness theorem for witnessed semantics will be stated.