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A fuzzy logic with interval truth values. (English) Zbl 0953.03029
The author studies Kenevan’s fuzzy logic (see the paper of J. R. Kenevan and R. E. Neapolitan, “A model theoretic approach to propositional fuzzy logic using Beth tableau” [in: L. A. Zadeh and J. Kacprzyk (eds.), Fuzzy logic for the management of uncertainty (Wiley, New York), 141-157 (1992)]). The truth values of the propositions in this logic are represented as subintervals of the real unit interval. The classical propositional logic is a particular case of this logic, when restricting the truth intervals to points. If the truth intervals are subintervals of the interval \((0.5,1)\), then this logic becomes Zadeh’s dispositional logic (a disposition is a proposition with truth value of probably true). The completeness and the computational complexity of this logic are also investigated. The author shows finally a truth interval predicate logic.
Reviewer: S.Sessa (Napoli)

MSC:
03B52 Fuzzy logic; logic of vagueness
68T37 Reasoning under uncertainty in the context of artificial intelligence
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