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

Abstract

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.

Spatio-Temporal Stream Reasoning with Adaptive State Stream Generation

“…Picking a single landmark corresponds to the case of adding a single connection between two disconnected RCC-8 networks for different time-points. The issue of choosing more than one landmark while retaining consistency is a difficult problem, and is closely related to the Amalgamation Property (Li et al, 2008), as well as the Patchwork Property (Lutz and Milicić, 2007;Huang, 2012).…”

Mobile Semantic-Based Matchmaking: A Fuzzy DL Approach

“…2. Relevant axioms in the fire prevention ontology used in the case study specific operators (e.g., the time domain with Allen's time interval relations or plane geometry with RCC8 relations [18]). …”

Towards spatial reasoning in fuzzy description logics

“…Syntax. Recall that ALCF(D) is the basic DL ALC extended with functional roles (letter F) and concrete domains [12] (letter D) allowing to deal with data types such as strings, integers and reals. In our specific fuzzy ALC(D), the concrete domain consists of the set of regions R and spatial relations over it.…”

“…We further need a technical definition involving features (see [12], [21]). Let F be a forest, f an abstract feature such that we have two edges v, w 1 and v, w 1 such that f occurs in both L( v, w 1 ) and L( v, w 2 ).…”