Abstract

In fuzzy predicate logic, assignment of truth values may be partial, i.e. the truth value of a formula in an interpretation may be undefined . A logic is supersound if each provable formula is true in each interpretation in which the truth value of is defined. It is shown that among the logics given by continuous t-norms, Gödel logic is the only one that is supersound; all others are not supersound. This supports the view that the usual restriction of semantics to safe interpretations is very natural