Maja Miličić

A Tableau Algorithm for Description Logics with Concrete Domains and General TBoxes

In order to use description logics (DLs) in an application, it is crucial to identify a DL that is sufficiently expressive to represent the relevant notions of the application domain, but for which reasoning is still decidable. Two means of expressivity required by many modern applications of DLs are concrete domains and general TBoxes. The former are used for defining concepts based on concrete qualities of their instances such as the weight, age, duration, and spatial extension. The purpose of the latter is to capture background knowledge by stating that the extension of a concept is included in the extension of another concept. Unfortunately, combining concrete domains with general TBoxes often leads to DLs for which reasoning is undecidable. In this paper, we identify a general property of concrete domains that is sufficient for proving decidability of DLs with both concrete domains and general TBoxes. We exhibit some useful concrete domains, most notably a spatial one based on the RCC-8 relations that have this property. Then, we present a tableau algorithm for reasoning in DLs equipped with concrete domains and general TBoxes.

A tableau algorithm for description logics with concrete domains and GCIs

In description logics (DLs), concrete domains are used for defining concepts based on concrete qualities of their instances such as the weight, age, duration, and spatial extension. So-called general concept inclusions (GCIs) play an important role for capturing background knowledge. It is well-known that, when combining concrete domains with GCIs, reasoning easily becomes undecidable. In this paper, we identify a general property of concrete domains that is sufficient for proving decidability of DLs with both concrete domains and GCIs. We exhibit some useful concrete domains, most notably a spatial one based on the RCC-8 relations, which have this property. Then, we present a tableau algorithm for reasoning in DLs equipped with concrete domains and GCIs.

Complexity of planning in action formalisms based on description logics

In this paper, we continue the recently started work on integrating action formalisms with description logics (DLs), by investigating planning in the context of DLs. We prove that the plan existence problem is decidable for actions described in fragments of ALCQIO. More precisely, we show that its computational complexity coincides with the one of projection for DLs between ALC and ALCQIO if operators contain only unconditional post-conditions. If we allow for conditional postconditions, the plan existence problem is shown to be in 2-ExpSpace.In this paper, we continue the recently started work on integrating action formalisms with description logics (DLs), by investigating planning in the context of DLs. We prove that the plan existence problem is decidable for actions described in fragments of ALCQIO. More precisely, we show that its computational complexity coincides with the one of projection for DLs between ALC and ALCQIO if operators contain only unconditional post-conditions. If we allow for conditional postconditions, the plan existence problem is shown to be in 2-ExpSpace.