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A note on the notion of truth in fuzzy logic

✍ Scribed by Petr Hájek; John Shepherdson

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
74 KB
Volume
109
Category
Article
ISSN
0168-0072

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✦ Synopsis

In fuzzy predicate logic, assignment of truth values may be partial, i.e. the truth value of a formula in an interpretation may be undeÿned (due to lack of some inÿnite suprema or inÿma in the underlying structure of truth values). A logic is supersound if each provable formula ' is true (has truth value 1) in each interpretation in which the truth value of ' is deÿned. It is shown that among the logics given by continuous t-norms, G odel 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 assignments is total) is very natural.

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