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 (due to lack of some infinite suprema or infima in the underlying structure of truth values). A logic is supersound if each provable formula p is true in each interpretation in which its truth value is defined. It is shown that among the logics given by continuous t-norms, Goedel logic is the only one that is supersound; all others are (sound but)not supersound. This supports the view that the usual restriction of semantics to safe interpretations (in which the truth assignment is total) is very natural.
|Translated title of the contribution||A note on the notion of truth in fuzzy logic|
|Pages (from-to)||65 - 69|
|Number of pages||5|
|Journal||Annals of Pure and Applied Logic|
|Publication status||Published - 2001|