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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)

03B52 Fuzzy logic; logic of vagueness
68T37 Reasoning under uncertainty in the context of artificial intelligence
Full Text: DOI
[1] Beth, E., The foundations of mathematics, (1959), North-Holland Amsterdam
[2] Chang, C.-L.; Lee, R.C-T., Symbolic logic and mechanical theorem proving, (1973), Academic Press New York · Zbl 0263.68046
[3] Chellas, B., Modal logic an introduction, (1980), Cambridge University Press Cambridge · Zbl 0431.03009
[4] Davis, R.E., Truth, deduction, and computation, (1989), Computer Science Press New York · Zbl 0823.68060
[5] Elfrink, B.; Reichgelt, H., Assertion time inference in logic-based systems, (), 112-142
[6] Kenevan, J.R.; Neapolitan, R.E., A model theoretic approach to propositional fuzzy logic using beth tableau, (), 141-157
[7] Loyd, J.W., Foundations of logic programming, (1984), Springer New York
[8] Mendelson, E., Introduction to mathematical logic, wadsworth and brooks/>cole advanced books and software, (1987), Monterey CA
[9] deSilva, C.J.S.; Attikiouzel, Y., A better path to duplicating human reasoning, IEEE expert, 9, 4, 14, (1994) · Zbl 1009.03520
[10] Smullyan, R.M., First-order logic, (1968), Springer New York · Zbl 0172.28901
[11] Turner, R., Logics for artificial intelligence, (1984), Ellis Horwood, West Sussex England
[12] Zadeh, L.A., Dispositional logic and commonsense reasoning, report CSL188-117, (1988), Center for the Study of Language and Information Stanford, CA · Zbl 0634.03020
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