On Correspondences between Probabilistic First-Order and Description Logics

This paper analyzes the probabilistic description logic PSHIQ by looking at it as a fragment of probabilistic first-order logic with semantics based on possible worlds. We argue that this is an appropriate way of investigating its properties and developing extensions. We show how the previously made arguments about different types of first-order probabilistic semantics apply to P-SHIQ. This approach has advantages for the future of both P-SHIQ, which can further evolve by incorporating semantic theories developed for the full first-order case, and the first-order logic, for which very few interesting decidable fragments are currently known. The paper also presents a probabilistic logic P-SHIQ which addresses some of the identified limitations of P-SHIQ.