Artificial Intelligence
Correctness criteria of some algorithms for uncertain reasoning using incidence calculus
Journal of Automated Reasoning
Incidence calculus: A mechanism for probabilistic reasoning
Journal of Automated Reasoning
Representing and reasoning with probabilistic knowledge: a logical approach to probabilities
Representing and reasoning with probabilistic knowledge: a logical approach to probabilities
Anytime deduction for probabilistic logic
Artificial Intelligence
Combination of compatible belief functions and relation of specificity
Advances in the Dempster-Shafer theory of evidence
Heuristic reasoning about uncertainty: an artificial intelligence approach
Heuristic reasoning about uncertainty: an artificial intelligence approach
On the combination of logical and probabilistic models for information analysis
Applied Intelligence
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Incidence calculus is a probabilistic logic in which incidences, standing for the situations in which formulae may be true, are assigned to some formulae, and probabilities are assigned to incidences. However, numerical values may be assigned to formulae directly without specifying the incidences. In this paper, we propose a method of discovering incidences under these circumstances which produces a unique output comparing with the large number of outputs from other approaches. Some theoretical aspects of this method are thoroughly studied and the completeness of the result generated from it is proved.The result can be used to calculate mass functions from belief functions in the Dempster-Shafer theory of evidence (DS theory) and define probability spaces from inner measures (or lower bounds) of probabilities on the relevant propositional language set.