Correctness criteria of some algorithms for uncertain reasoning using Incidence Calculus

Abstract

Incidence Calculus is a technique for associating uncertainty values with logical sentences. These uncertainty values are called incidences and they are sets of points, which may be thought of as representing equivalence classes of situations, Tarskian models, or possible worlds. Incidence Calculus was originally introduced in [1]. Incidence Calculus was designed to overcome various inherent problems with purely numeric mechanisms for uncertain reasoning [2]. In particular, incidences can represent the dependence between sentences, which numbers cannot, and hence Incidence Calculus can provide genuine, probabilistic reasoning. In this paper we prove soundness and completeness results for some algorithms introduced in [1] and hence satisfy some of the correctness criteria for Incidence Calculus. These algorithms can be used for probabilistic reasoning and to check the consistency of the subjective probabilities of sentences.