Abstract
In this paper, given an arbitrary finite family of conditional events F, a generalized probabilistic knowledge base represented by a set of conditional probability bounds defined on F is considered. Following the approach of de Finetti we define the concept of coherence for the given set of bounds. Then, some results on the probabilistic consistency of the knowledge base are obtained. Finally, an algorithm to check the coherence of the set of bounds is described and some examples are examined.
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References
E. W. Adams: The logic of conditionals. Dordrecht: Reidel, 1975
G. Coletti: Coherent numerical and ordinal probabilistic assessments, IEEE Transactions on Systems, Man, and Cybernetics 24, n. 12, 1747–1754 (1994)
G. Coletti: Numerical and qualitative judgements in probabilistic expert systems. In: R. Scozzafava (ed.): Probabilistic Methods in Expert Systems. Roma: S.I.S. 1993, pp. 37–55
G. Coletti, A. Gilio, R. Scozzafava: Conditional events with vague information in expert systems. In: B. Bouchon-Meunier, R. R. Yager, L. A. Zadeh (eds.): Uncertainty in Knowledge Bases. Lecture Notes in Computer Science 521. Berlin: Springer 1991, pp. 106–114
G. Coletti, A. Gilio, R. Scozzafava: Comparative probability for conditional events: a new look through coherence. Theory and Decision 35, 237–258 (1993)
L. M. De Campos, J. F. Huete: Learning non probabilistic belief networks. In: (M. Clarke, R. Kruse, S. Moral (eds.): Symbolic and Quantitative Approaches to Reasoning and Uncertainty. Lecture Notes in Computer Science 747. Berlin: Springer 1993, pp. 57–64
B. de Finetti: Theory of probability, 2 Volumes (A.F.M. Smith and A. Machítrs.). New York: John Wiley 1974, 1975
D. Dubois, H. Prade: Probability in automated reasoning: from numerical to symbolic approaches. In: R. Scozzafava (ed.): Probabilistic Methods in Expert Systems. Roma: S.I.S. 1993, pp. 79–104.
D. Dubois, H. Prade, L. Godo, R. L. De Mántaras: Qualitative reasoning with imprecise probabilities. Journal of Intelligent Information Systems 2, 319–362 (1993)
A. Gilio: Criterio di penalizzazione e condizioni di coerenza nella valutazione soggettiva della probabilita'. Boll. Un. Matem. Ital.(7) 4-B, 645–660 (1990)
A. Gilio: Algorithms for precise and imprecise conditional probability assessments. In: G. Coletti, R. Scozzafava, D. Dubois (eds.): ”Mathematical Models for Handling Partial Knowledge in Artificial Intelligence”, London: Plenum Publ. Co. 1995 (to appear)
A. Gilio: Probabilistic consistency of knowledge bases in inference systems. In: M. Clarke, R. Kruse, S. Moral (eds.): Symbolic and Quantitative Approaches to Reasoning and Uncertainty. Lecture Notes in Computer Science 747. Berlin: Springer 1993, pp. 160–167
A. Gilio, R. Scozzafava: Le probabilita' condizionate coerenti nei sistemi esperti. In: Atti Giornate di lavoro A.I.R.O. su ”Ricerca Operativa e Intelligenza Artificiale”, Pisa: IBM 1988, pp. 317–330
A. Gilio, R. Scozzafava: Conditional events in probability assessment and revision. IEEE Transactions on Systems, Man, and Cybernetics 24, n. 12, 1741–1746 (1994)
A. Gilio, F. Spezzaferri: Knowledge integration for conditional probability assessments. In: D. Dubois, M. P. Wellman, B. D'Ambrosio, P. Smets (eds.): Uncertainty in Artificial Intelligence, San Mateo, California: Morgan Kaufmann Publishers 1992, pp. 98–103.
G.D. Kleiter: Expressing imprecision in probabilistic knowledge. In: Scozzafava (ed.): Probabilistic Methods in Expert Systems. Roma: S.I.S. 1993, pp. 139–158
S. Moral: A formal language for convex sets of probabilities. In: M. Clarke, R. Kruse, S. Moral (eds.): Symbolic and Quantitative Approaches to Reasoning and Uncertainty. Lecture Notes in Computer Science 747 Berlin: Springer 1993, pp. 274–281
R. Scozzafava: Subjective probability versus belief functions in artificial intelligence. International Journal of General Systems 22, 197–206 (1994)
R. Scozzafava: How to solve some critical examples by a proper use of coherent probability. In: B. Bouchon-Meunier, L. Valverde, R. R. Yager (eds.): Uncertainty in Intelligent Systems. North-Holland: Elsevier Science Publ. B. V. 1993, 121–132
H. Thöne, U. Güntzer, W. Kießling: Towards precision of probabilistic bounds propagation. In: D. Dubois, M. P. Wellman, B. D'Ambrosio, P. Smets (eds.): Uncertainty in Artificial Intelligence, San Mateo, California: Morgan Kaufmann Publishers 1992, pp.315–322
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Gilio, A. (1995). Probabilistic consistency of conditional probability bounds. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Advances in Intelligent Computing — IPMU '94. IPMU 1994. Lecture Notes in Computer Science, vol 945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035951
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DOI: https://doi.org/10.1007/BFb0035951
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