Practical Issues of Description Logics for Spatial Reasoning

Matteo Cristani, Nicoletta Gabrielli

Spatial reasoning with description logic has become an im- portant research topic in the recent past. Several authors dealt with the problem of finding logical frameworks in which concept definitions can be made by using also spatial opera- tors, particularly those of the Region Connection Calculus. Lutz and Milicic investigated the formal properties required to the concrete domain of the logical structure ALC(C) to accommodate decidable reasoning. These properties, named the patchwork property and the compactness property, along with the decidability of the constraint system C guarantee the condition of ω-admissibility which, in turn, guarantees decidability of ALC(C). Lutz and Milicic also proved that ALC (RCC8) is decidable. The expressiveness of this system is enough to define interesting concepts, but other frame- works result useful too. We investigate the combination of ALC(C) with the Cardinal Direction Calculus defined by Ligozat and propose an extension based on a combined constraint system formed by the Region Connection Calculus and the Cardinal Direction Calculus recently studied by Li. We prove that the mentioned reasoning systems are useful by comparing their expressiveness in translating natural language sentences describing concepts of common usage.

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