Fuzzy logic and approximate reasoning

Synthese 30 (3-4):407-428 (1975)
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Abstract

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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Citations of this work

Being Realist about Bayes, and the Predictive Processing Theory of Mind.Matteo Colombo, Lee Elkin & Stephan Hartmann - 2021 - British Journal for the Philosophy of Science 72 (1):185-220.
Bayesian Cognitive Science, Monopoly, and Neglected Frameworks.Matteo Colombo & Stephan Hartmann - 2015 - British Journal for the Philosophy of Science 68 (2):451–484.
A truth maintenance system.Jon Doyle - 1979 - Artificial Intelligence 12 (3):231-272.
Probabilistic logic.Nils J. Nilsson - 1986 - Artificial Intelligence 28 (1):71-87.

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References found in this work

From a Logical Point of View.Willard Van Orman Quine - 1953 - Cambridge: Harvard University Press.
Logic, semantics, metamathematics.Alfred Tarski - 1956 - Oxford,: Clarendon Press. Edited by John Corcoran & J. H. Woodger.
Many-valued logic.Nicholas Rescher - 1969 - New York,: McGraw-Hill.
The logic of inexact concepts.J. A. Goguen - 1969 - Synthese 19 (3-4):325-373.
Fuzzy Sets.Lofti A. Zadeh - 1965 - Information and Control 8 (1):338--53.

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