Local Probabilistic Deduction from Taxonomic and Probabilistic Knowledge−Bases over Conjunctive Events

Abstract

We elaborate locally complete inference rules for probabilistic deduction from taxonomic and probabilistic knowledge-bases over conjunctive events. We integrate the presented inference rules into a local probabilistic deduction technique, which exploits taxonomic knowledge for an efficient representation of conjunctive events. This local probabilistic deduction technique is less incomplete and more efficient than already existing local approaches to probabilistic deduction. However, we show that it cannot compete with global probabilistic deduction by linear programming. Surprisingly, we can provide examples of globally very incomplete probabilistic deductions in the presented local approach. More generally, we even show that all systems of inference rules for probabilistic deduction in taxonomic and probabilistic knowledge-bases over conjunctive events that have a limited number of probabilistic formulas in the premises of their inference patterns are globally incomplete. Furthermore, we show that the presented local approach is not more efficient than the linear programming approach for that framework. We conclude that probabilistic deduction by the iterative application of inference rules on interval restrictions for conditional probabilities, even though considered very promising in the literature so far, is very limited in its field of application.