Probabilistic Description Logics

TL;DR

This paper introduces ACP, a probabilistic extension of terminological logics, enabling reasoning with uncertain concept descriptions while maintaining logical consistency, bridging the gap between classical knowledge representation and probabilistic reasoning.

Contribution

It presents the formal semantics and probabilistic formalism of ALUP, integrating probabilistic constraints with terminological knowledge for consistent uncertain reasoning.

Findings

Formal semantics for ALUP established

Probabilistic constraints ensure consistency

Enables reasoning with uncertain terminological knowledge

Abstract

On the one hand, classical terminological knowledge representation excludes the possibility of handling uncertain concept descriptions involving, e.g., "usually true" concept properties, generalized quantifiers, or exceptions. On the other hand, purely numerical approaches for handling uncertainty in general are unable to consider terminological knowledge. This paper presents the language ACP which is a probabilistic extension of terminological logics and aims at closing the gap between the two areas of research. We present the formal semantics underlying the language ALUP and introduce the probabilistic formalism that is based on classes of probabilities and is realized by means of probabilistic constraints. Besides inferring implicitly existent probabilistic relationships, the constraints guarantee terminological and probabilistic consistency. Altogether, the new language ALUP applies to domains where both term descriptions and uncertainty have to be handled.