Journal of Logic and Computation Advance Access published online on March 18, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp013
Original Papers |
Models for Many-Valued Probabilistic Reasoning
Department of Mathematics and Computer Science, University of Siena, Pian dei Matellini 44, 53100 Siena, Italy.
E-mail: flaminio{at}unisi.it; montagna{at}unisi.it
Received 2 October 2008.
In this article, we compare models for many-valued probabilistic reasoning from the point of view of the sets of satisfiable formulas, positive satisfiable formulas, and tautologies. The results arising from this comparison will be used in the final part of the present article to provide results about the computational complexity for the problem of deciding if a formula belongs to one of the previously discussed sets.
Keywords: SMV-algebras; states on MV-algebras; probabilistic Kripke models; PSPACE containment
References
- Blok W, Pigozzi D. Algebraizable Logics. Memoirs of the American Mathematical Society (1989) 396:77.
- Canny JF. Some algebraic and geometric computations in PSPACE. (1988) 460–467. In Proceedings of 20th ACM Symposium on Theory of Computing.
- Chang CC. Algebraic analysis of many-valued logics. Transactions of the American Mathematical Society (1958) 88:467–490.[CrossRef]
- Cignoli R, DOttaviano IML, Mundici D. Algebraic Foundations of Many-valued Reasoning (2000) Kluwer.
- de Finetti B. Sul signicato soggettivo della probabilità. Fundamenta Mathematicae (1931) 17:298–329. Translated into English as "On the subjective meaning of probability", In Probabilità e Induzione, P. Monari and D. Cocchi, eds, pp. 291–321, Clueb, Bologna, 1993.
- Flaminio T, Godo L. A logic for reasoning on the probability of fuzzy events. Fuzzy Sets and Systems (2007) 158:625–638.[CrossRef][Web of Science]
- Flaminio T, Montagna F. An algebraic approach to states on MV-algebras. In: Proceedings of EUSFLAT07—
t
pni
ka M, Novák V, Bodenhofer U, eds. (2007) 2:201–2006. - Flaminio T, Montagna F. MV-algebras with internal states and probabilistic fuzzy logics. International Journal of Approximate Reasoning (2009) 50:138–152.[CrossRef][Web of Science]
- Hájek P. Metamathematics of Fuzzy Logic (1998) Kluwer Academy Press.
- Kühr J, Mundici D. De Finetti theorem and Borel states in [0,1]-valued algebraic logic. International Journal of Approximate Reasoning (2007) 46:605–616.[CrossRef][Web of Science]
- Montagna F. Subreducts of MV-algebras with product and product residuation. Algebra Universalis (2005) 53:109–137.[CrossRef][Web of Science]
- Montagna F, Panti G. Adding structure to MV-algebras. Journal of Pure and Applied Algebra (2001) 164:365–387.[CrossRef][Web of Science]
- Mundici D. Averaging the truth-value in
ukasiewicz logic. Studia Logica (1995) 55:113–127.[CrossRef] - Mundici D. Tensor products and the Loomis-Sikorski theorem for MV-algebras. Advances in Applied Mathematics (1999) 22:227–248.[CrossRef][Web of Science]
- Mundici D. Bookmaking over infinite-valued events. International Journal of Approximate Reasoning (2006) 46:223–240.
| ||||||||||||||||||||||||||||||||||||||||||||||||||