Abstract
In incidence calculus, inferences usually are made by calculating incidence sets and probabilities of formulae based on a given incidence function in an incidence calculus theory. However it is still the case that numerical values are assigned on some formulae directly without giving the incidence function. This paper discusses how to recover incidence functions in these cases. The result can be used to calculate mass functions from belief functions in the Dempster-Shafer theory of evidence (or DS theory) and define probability spaces from inner measures (or lower bounds) of probabilities on the relevant propositional language set.
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References
Bundy,A., Incidence calculus: a mechanism for probability reasoning, J. of Automated Reasoning. 1, 263–283, 1985.
Bundy,A., Correctness criteria of some algorithms for uncertain reasoning using incidence calculus., J. of Automated reasoning. 2 109–126., 1986.
Bundy,A., Incidence Calculus, The Encyclopedia of AI, 663–668, 1992. It is also available as the Research paper No. 497 in the Dept. of Artificial Intelligence, Univ. of Edinburgh.
Correa da Silva,F. and A.Bundy, On some equivalent relations between incidence calculus and Dempster-Shafer theory of evidence, Proc. of sixth workshop of Uncertainty in Artificial Intelligence. 378–383, 1990.
Fagin,R. and J. Halpern, Uncertainty, belief and probability, Research Report of IBM, RJ 6191, 1989.
Kennes,R. Computational aspects of the Moebius transform of a graph, IEEE-SMC, 22:201–223, 1991.
Kennes,R. and Smets,Ph., Computational aspects of the Moebius Transform. Proc. of the 6th Conf. on Uncertainty in AI Eds. by P.Bonissone, M.Henrion, L.Kanal and J.Lemmer. Cambridge, MA. North Holland, 401–416, 1990a.
Liu,W., Incidence calculus and generalized incidence calculus. Chapter 2 of a forthcoming PhD thesis. Dept. of AI, Univ. of Edinburgh, 1993.
Liu,W. and A.Bundy, The combination of different pieces of evidence using incidence calculus, Research Paper 599, Dept. of Artificial Intelligence, Univ. of Edinburgh, 1992.
Liu,W., A.Bundy and D.Robertson, On the relationship between incidence calculus and the ATMS, in this proceedings, 1993.
Liu, W., A.Bundy and D.Robertson, Recovering incidence functions, forthcoming departmental research paper, 1993.
McLean,R.G., Testing and Extending the Incidence Calculus, M.Sc. Dissertation, Dept. of Artificial Intelligence, Univ. of Edinburgh, 1992.
Shafer,G., A mathematical theory of evidence, Princeton University Press. 1976.
Smets,P., Belief functions, Non-Standard Logics for Automated Reasoning, (Smets, Mamdani, Dubois and Prade Eds.), 253–286, 1988.
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© 1993 Springer-Verlag Berlin Heidelberg
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Liu, W., Bundy, A., Robertson, D. (1993). Recovering incidence functions. In: Clarke, M., Kruse, R., Moral, S. (eds) Symbolic and Quantitative Approaches to Reasoning and Uncertainty. ECSQARU 1993. Lecture Notes in Computer Science, vol 747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028206
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DOI: https://doi.org/10.1007/BFb0028206
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