Fuzzy logic and approximate reasoning

Synthese 30 (3-4):407-428 (1975)
The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc. The truth-value set, , of FL is assumed to be generated by a context-free grammar, with a semantic rule providing a means of computing the meaning of each linguistic truth-value in as a fuzzy subset of [0, 1].Since is not closed under the operations of negation, conjunction, disjunction and implication, the result of an operation on truth-values in requires, in general, a linguistic approximation by a truth-value in . As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very, quite, more or less, etc.
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DOI 10.1007/BF00485052
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Elia Zardini (2008). A Model of Tolerance. Studia Logica 90 (3):337 - 368.
Joseph Y. Halpern (2008). Intransitivity and Vagueness. Review of Symbolic Logic 1 (4):530-547.

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