Abstract
We consider a finite family of conditional events and, among other results, we prove a connection property for the set of coherent assessments on such family. This property assures that, for every pair of coherent assessments on the family, there exists (at least) a continuous curve C whose points are intermediate coherent probability assessments. We also consider the compactness property for the set of coherent assessments. Then, as a corollary of connection and closure properties, we obtain the theorem of extension for coherent conditional probabilities.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Biazzo, V., Gilio, A.: A generalization of the fundamental theorem of de Finetti for imprecise conditional probability assessments. International Journal of Approximate Reasoning 24, 251–272 (2000)
Biazzo, V., Gilio, A.: On the linear structure of betting criterion and the checking of coherence. Annals of Mathematics and Artificial Intelligence 35, 83–106 (2002)
Biazzo, V., Gilio, A., Lukasiewicz, T., Sanfilippo, G.: Probabilistic Logic under Coherence, Model-Theoretic Probabilistic Logic, and Default Reasoning in System P. Journal of Applied Non-Classical Logics 12(2), 189–213 (2002)
Biazzo, V., Gilio, A., Sanfilippo, G.: Coherence Checking and Propagation of Lower Probability Bounds. Soft Computing 7, 310–320 (2003)
Biazzo, V., Gilio, A., Sanfilippo, G.: On the checking of g-coherence of conditional probability bounds. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11(Suppl. 2), 75–104 (2003)
Capotorti, A., Vantaggi, B.: Locally strong coherence in inferential processes. Annals of Mathematics and Artificial Intelligence 35: 125–149 (2002)
Coletti, G.: Coherent numerical and ordinal probabilistic assessments. IEEE Trans. on Systems, Man, and Cybernetics 24(12), 1747–1754 (1994)
Coletti, G., Scozzafava, R.: Characterization of coherent conditional probabilities as a tool for their assessment and extension. Journal of Uncertainty. Fuzziness and Knowledge-based Systems 4(2), 103–127 (1996)
Coletti, G., Scozzafava, R.: Conditioning and inference in intelligent systems. Soft Computing 3(3), 118–130 (1999)
Coletti, G., Scozzafava, R.: Probabilistic logic in a coherent setting. Kluwer Academic Publishers, Dordrecht (2002)
Gale, D.: The theory of linear economic models. McGraw-Hill, New York (1960)
Gilio, A.: Algorithms for precise and imprecise conditional probability assessments. In: Coletti, G., Dubois, D., Scozzafava, R. (eds.) Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, pp. 231–254. Plenum Press, New York (1995)
Holzer, S.: On coherence and conditional prevision, Boll. U.M.I., Serie VI, Vol. IV-C(1), pp. 441-460 (1985)
Pelessoni, R., Vicig, P.: A consistency problem for imprecise conditional probability assessments. In: Proc. of the Seventh Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 1998), Paris, France, 1478-1485 (1998)
Scozzafava, R.: Subjective conditional probability and coherence principles for handling partial information. Mathware Soft Comput. 3, 183–192
Vicig, P.: An algorithm for imprecise conditional probability assessments in expert systems. In: Proc. of the Sixth Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 1996), Granada, Spain, pp. 61–66 (1996)
Walley, P.: Statistical reasoning with imprecise probabilities. Chapman and Hall, London (1991)
Walley, P., Pelessoni, R., Vicig, P.: Direct Algorithms for Checking Coherence and Making Inferences from Conditional Probability Assessments. Journal of Statistical Planning and Inference 126(1), 119–151 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Biazzo, V., Gilio, A. (2005). Some Theoretical Properties of Conditional Probability Assessments. In: Godo, L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2005. Lecture Notes in Computer Science(), vol 3571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11518655_65
Download citation
DOI: https://doi.org/10.1007/11518655_65
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27326-4
Online ISBN: 978-3-540-31888-0
eBook Packages: Computer ScienceComputer Science (R0)