A note on the notion of truth in fuzzy logic

JC Shepherdson; P Hajek

A note on the notion of truth in fuzzy logic

JC Shepherdson
, P Hajek

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

5 Citations (Scopus)

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

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title = "A note on the notion of truth in fuzzy logic",

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.",

author = "JC Shepherdson and P Hajek",

year = "2001",

language = "English",

volume = "109",

pages = "65 -- 69",

journal = "Annals of Pure and Applied Logic",

publisher = "Elsevier B.V.",

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T1 - A note on the notion of truth in fuzzy logic

AU - Shepherdson, JC

AU - Hajek, P

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

M3 - Article (Academic Journal)

VL - 109

SP - 65

EP - 69

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

ER -

A note on the notion of truth in fuzzy logic

Abstract

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