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This paper introduces a formal method for integrating knowledge derived from a variety of sources for use in ``perceptual reasoning.’’ The formalism is based on the ``evidential propositional calculus.’’ a derivative of Shafer’s mathematical theory of evidence [Shafer 1976]. It is more general than either a Boolean or Bayesian approach, providing for Boolean and Bayesian inferencing when the appropriate information is available. In this formalism, the likelihood of a proposition A is represented as a subinterval, [s(A),p(A)], of the unit interval [0,1]. The evidential support for the proposition A is represented by s(A), while p(A) represents its degree of plausibility; p(A) can also be interpreted as the degree to which one fails to doubt A, p(A) being equal to one minus the evidential support for ~A. This paper describes how evidential information, furnished by a knowledge source in the form of a probability ``mass’’ distribution, can be converted to this interval representation; how, through a set of inference rules for computing intervals of dependent propositions, this information can be extrapolated from those propositions it directly bears upon, to those it indirectly bears upon; and how multiple bodies of evidential information can be pooled. A sample application of this approach, modeling the operation of a collection of sensors (a particular type of knowledge source), illustrates these techniques.
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