A hybrid approach for modeling uncertainty in terminological logics

This paper proposes a probabilistic extension of terminological logics. The extension maintains the original performance of drawing inferences in a hierarchy of terminological definitions. It enlarges the range of applicability to real world domains determined not only by definitional but also by uncertain knowledge. First, we introduce the propositionally complete terminological language ALC. On the basis of the language construct "probabilistic implication" it is shown how statistical information on concept dependencies can be represented. To guarantee (terminological and probabilistic) consistency, several requirements have to be met. Moreover, these requirements allow one to infer implicitly existent probabilistic relationships and their quantitative computation. By explicitly introducing restrictions for the ranges derived by instantiating the consistency requirements, exceptions can also be handled. In the categorical cases this corresponds to the overriding of properties in non monotonic inheritance networks. Consequently, our model applies to domains where both term descriptions and non-categorical relations between term extensions have to be represented

Modelling default and likelihood reasoning as probabilistic

A probabilistic analysis of plausible reasoning about defaults and about likelihood is presented. 'Likely' and 'by default' are in fact treated as duals in the same sense as 'possibility' and 'necessity'. To model these four forms probabilistically, a logic QDP and its quantitative counterpart DP are derived that allow qualitative and corresponding quantitative reasoning. Consistency and consequence results for subsets of the logics are given that require at most a quadratic number of satisfiability tests in the underlying propositional logic. The quantitative logic shows how to track the propagation error inherent in these reasoning forms. The methodology and sound framework of the system highlights their approximate nature, the dualities, and the need for complementary reasoning about relevance