Extended incidence calculus and its comparison with related theories
This thesis presents a comprehensive study o f incidence calculus, a probabilistic logic for reasoning under uncertainty which extends two-value propositional logic to a multiple-value logic. There are three main contributions in this thesis.First of all, the original incidence calculus is extended considerably in three aspects: (a) the original incidence calculus is generalized; (b) an efficient algorithm for incidence assignment based on generalized incidence calculus is developed; (c) a combination rule is proposed for the combination of both independent and some dependent pieces of evidence. Extended incidence calculus has the advantages of representing information flexibly and combining multiple sources o f evidence.Secondly, a comprehensive comparison between extended incidence calculus and the Dempster-Shafer (DS) theory of evidence is provided. It is proved that extended incidence calculus is equivalent to DS theory in representing evidence and combining independent evidence but superior to DS theory in combining dependent evidence.Thirdly, the relations between extended incidence calculus and the assumption- based truth maintenance systems are discussed. It is proved that extended incidence calculus is equivalent to the ATM S in calculating labels for nodes. Extended incidence calculus can also be used as a basis for constructing probabilistic ATMSs.The study in this thesis reveals that extended incidence calculus can be regarded as a bridge between numerical and symbolic reasoning mechanisms.