The University of Edinburgh -
Division of Informatics
Forrest Hill & 80 South Bridge

MSc Thesis #92135

Title:Testing and Extending the Incidence Calculus
Date: 1992
Abstract:Incidence calculus is a mechanism for probabilistic reasoning developed by A. Bundy. Many approaches to uncertain reasoning in artificial intelligence associate numbers directly with logical formulae and are difficult to justify using standard probability theory. In incidence calculus sets of possible worlds, called incidences, are associated with axioms and probabilities are then associated with these sets. Inference rules are used to deduce bounds on the incidences of formulae which are not axioms and bounds for the probability of such a formula can then be obtained. In this work is shown that the task of assigning incidences can be viewed as a tree searching problem and two techniques for performing this search are discussed. One of these uses a depth first search while the other incorporates a suitable random element. The two approaches are compared for efficiency and the significance of their results is discussed. In addition we give inference rules for the logical connectives describing disjunction and implication which add to the rules for negation and conjunction given by Bundy. Finally we investigate connections between linear programming and the estimation of probabilities in incidence calculus.

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