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 (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 |
|---|---|
| Original language | English |
| Pages (from-to) | 65 - 69 |
| Number of pages | 5 |
| Journal | Annals of Pure and Applied Logic |
| Volume | 109 |
| Publication status | Published - 2001 |