A note on the notion of truth in fuzzy logic

JC Shepherdson, P Hajek

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)


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 contributionA note on the notion of truth in fuzzy logic
Original languageEnglish
Pages (from-to)65 - 69
Number of pages5
JournalAnnals of Pure and Applied Logic
Publication statusPublished - 2001


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