Measuring conflict and agreement between two prioritized knowledge bases in possibilistic logic

In this paper we investigate the relationship between two prioritized knowledge bases by measuring both the conflict and the agreement between them. First of all, a quantity of conflict and two quantities of agreement are defined. The former is shown to be a generalization of the well-known Dalal distance which is the Hamming distance between two interpretations. The latter are, respectively, a quantity of strong agreement which measures the amount of information on which two belief bases “totally” agree, and a quantity of weak agreement which measures the amount of information that is believed by one source but is unknown to the other. All three quantity measures are based on the weighted prime implicant, which represents beliefs in a prioritized belief base. We then define a degree of conflict and two degrees of agreement based on our quantity of conflict and quantities of agreement. We also consider the impact of these measures on belief merging and information source ordering.