×

zbMATH — the first resource for mathematics

Complexity of fuzzy probability logics. II. (English) Zbl 1124.03008
Summary: The distinction between fuzzy logic in broad and narrow sense as well between fuzzy logic and probability theory is to be always stressed; but building bridges is wanted. We survey one of the possibilities – the logic of the fuzzy notion on being probable. We quickly survey the existing literature and present some new results on the computational complexity of several particular logics of “probably”.
For Part I by P. Hájek and S. Tulipani see Fundam. Inform. 45, No. 3, 207–213 (2001; Zbl 0972.03025).

MSC:
03B52 Fuzzy logic; logic of vagueness
03D15 Complexity of computation (including implicit computational complexity)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J.F. Canny, Some algebraic and geometric computations in PSPACE, in: Proc. 20th ACM Symp. on Theory of Computing, 1988, pp. 460-467.
[2] Fagin, R.; Halpern, J.Y.; Megido, N., A logic for reasoning about probabilities, Inform. comput., 87, 78-128, (1990) · Zbl 0811.03014
[3] Flaminio, T., A zero-layer based fuzzy probabilistic logic for conditional probability, (), 714-725 · Zbl 1109.03018
[4] Flaminio, T.; Godo, L., A logic for reasoning about probability of fuzzy events, Fuzzy sets and systems, 158, 625-638, (2007) · Zbl 1116.03018
[5] Flaminio, F.; Montagna, F., A logical and probabilistic treatment on conditional probability, Arch. math. logic, 44, 245-262, (2005) · Zbl 1064.03016
[6] Godo, L.; Esteva, F.; Hájek, P., Reasoning about probability using fuzzy logic, Neural network world, 10, 811-824, (2000)
[7] Godo, L.; Marchioni, E., Coherent conditional probability in a fuzzy logic setting, Logic J. IGPL, 14, 457-481, (2006) · Zbl 1117.03031
[8] Hájek, P., Metamathematics of fuzzy logic, (1998), Kluwer Academic Publishers Dordrecht · Zbl 0937.03030
[9] Hájek, P.; Godo, L.; Esteva, F., Fuzzy logic and probability, (), 237-244
[10] Hájek, P.; Tulipani, S., Complexity of fuzzy probability logics, Fund. inform., 45, 207-213, (2001) · Zbl 0972.03025
[11] T. Kroupa, States and conditional probability on MV-algebras, Dissertation, Czech Technical Unviersity, 2005.
[12] Kroupa, T., Representation and extension of states on MV-algebras, Arch. math. logic, 45, 381-392, (2006) · Zbl 1101.06008
[13] Mundici, D., Bookmaking over infinite-valued events, Internat. J. approx. reason., 43, 223-240, (2006) · Zbl 1123.03011
[14] Schrijver, A., Theory if linear and integral programming, (1968), Wiley New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.