**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.

2005-05-23