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

Re-investigating Dempster's idea on evidence combination.

Abstract. In this paper, we investigate the problem encountered by Dempster’s combination rule in view of Dempster’s original combination framework. We first show that the root of Dempster’s combination rule (defined and named by Shafer) is Dempster’s original idea on evidence combination. We then argue that Dempster’s original idea on evidence combination is, in fact, richer than what has been formulated in the rule. We conclude that, by strictly following what Dempster has suggested, there should be no counterintuitive results when combining evidence

Modifications of the Miller definition of contrastive (counterfactual) explanations

Miller recently proposed a definition of contrastive (counterfactual) explanations based on the well-known Halpern-Pearl (HP) definitions of causes and (non-contrastive) explanations. Crucially, the Miller definition was based on the original HP definition of explanations, but this has since been modified by Halpern; presumably because the original yields counterintuitive results in many standard examples. More recently Borner has proposed a third definition, observing that this modified HP definition may also yield counterintuitive results. In this paper we show that the Miller definition inherits issues found in the original HP definition. We address these issues by proposing two improved variants based on the more robust modified HP and Borner definitions. We analyse our new definitions and show that they retain the spirit of the Miller definition where all three variants satisfy an alternative unified definition that is modular with respect to an underlying definition of non-contrastive explanations. To the best of our knowledge this paper also provides the first explicit comparison between the original and modified HP definitions.Comment: Accepted by ECSQARU'2