The Web Ontology Language has not been designed for representing spatial information, which is often required for applications such as Spatial Databases and Geographical Information Systems. As a consequence, many existing OWL ontologies have little success in encoding spatial information. In this paper, we argue that the representation of spatial information is not a fundamental limitation of OWL. In fact, OWL-DL does provide some of the expressive power required for representation of spatial regions and their relationships. However, a direct representation is far from intuitive. In the last decade, several languages for the representation of the relations between spatial regions have been developed. Among these formalisms for qualitative spatial reasoning, the RCC-8 fragment of the Region Connection Calculus, which introduces a set of eight basic relationships between regions on the plane, has received special attention. In this paper, we outline a translation of the RCC-8 calculus into OWL-DL, by adapting some of the known results on the translation of qualitative spatial formalisms into Modal Logics. We argue that, in order to encode RCC-8, it is necessary to extend the Web Ontology Language with the ability to define reflexive roles1. However, such an extension is straightforward in both syntax and semantics, and can be easily added to existing OWL reasoners. We argue that providing a reasonable encoding of RCC related calculi into OWL-DL is key for integrating spatial representation and reasoning features in OWL-based tools, which can be helpful for many applications.
Description Logic S (ALC extended with transitive roles), augmented with a reflexive accessibility relation, yields the Modal Logic S4. It has also been shown that it is possible to translate the RCC-8 calculus and some of its extensions into S4 and its extension with the universal modality, called S4u. Relying on the correspondence between the two groups of formalisms, every S4 formula can be represented in OWL-DL provided that OWL-DL is extended with the ability to define reflexive roles, required for accommodating the reflexive/transitive accessibility relation of S4. Consequently, the translation into the extension of OWL-DL involves a single role that is both reflexive and transitive. OWL-DL extended in this way is expressive enough for capturing the RCC-8 calculus as well as some of its extensions.
The following issues immediately arise: first, is it easy to extend OWL-DL with reflexive roles? And second, will existing OWL reasoners exhibit an acceptable performance on (translated) spatial KBs? 2.1
A region is the set of points on the plane delimited by a continuous boundary curve. The RCC-8 calculus provides eight binary predicates for representing relationships between two regions X, Y . The regions X, Y are disconnected, written DC(X, Y ), if they do not share any points; they are externally connected (EC(X, Y )) if they only share points in their boundary. They are equal (EQ(X, Y )) if they contain exactly the same points; they “partially overlap” if their interiors intersect but none is a subset of the other; the region X is a tangential proper part of Y (T P P (X, Y )) if X is a subset of Y but not of its interior. Finally, X is a non-tangential proper part of Y if it is contained in the interior of Y . Note that the only asymmetric relations are T P P and N T P P and hence their inverses T P P −1(Y, X) and N T P P −1(X, Y ) can also hold between X and Y .
A role R is reflexive if, for every model I of the ontology, the following condition holds: If (x, y) ∈ RI then (x, x) ∈ RI . The syntax of OWL-DL can be trivially extended with a new primitive owl:ReflexiveProperty, analogous to the ones already existing in OWL-DL for tagging a role as symmetric and transitive.
On the other hand, extending an OWL-DL reasoner to handle reflexive roles is easy. We just have to take into consideration that every node of the completion graph with an incoming or outgoing R-edge, with R reflexive, is an R-successor of itself and apply the tableau expansion rules accordingly. 2.3
Our translation is a variation of the one in [
The translation proceeds in two steps: (1) we generate the concepts corresponding to every RCC-8 constructor, some of which will be uniquely named concepts not appearing elsewhere in the KB (denoted by Zn), and (2) we instantiate the named concepts with individuals. For brevity we show the translation of only six RCC-8 constructors (omitting inverses2): i. DC(X, Y ) :- X v ¬Y ii. EQ(X, Y ) :- X ≡ Y iii. EC(X, Y ) :- ∀R.X v ∃R.¬Y ; Z1 ≡ X u Y iv. P O(X, Y ) :- Z2 ≡ ∀R.X u ∀R.Y ; Z3 ≡ X u ¬Y ; Z4 ≡ ¬X u Y v. T P P (X, Y ) :- X v Y ; Z5 ≡ X u ∃R.¬Y vi. N T P P (X, Y ) :- X v ∀R.Y
Then, for every newly generated concept Zn, add the ABox assertion Zn(zn), where zn is a new individual name, in order to make sure that Zn cannot be empty without making the KB inconsistent. 3 3.1
A translation of the RCC-8 calculus into OWL makes it possible to adapt OWLbased tools for representing and reasoning on qualitative spatial information. In particular, ontology editors could be equipped with suitable user interfaces for 2 The constructors N T P P −1 and T P P −1 are translated exactly as their inverses above spatial modeling and spatial KBs could be published and shared on the Semantic Web.
On the other hand, the ability to use existing OWL reasoners, such as RACER, Pellet or FaCT, directly on spatial KBs raises a number of interesting issues for future research: Will existing DL optimizations work well for our translation? If not, is it possible to find an alternative translation for which DL optimizations work better or to design new optimization techniques for OWLencoded spatial KBs? In order to answer these questions, we are planning to provide in the near future an implementation in our OWL reasoner Pellet.
An even more relevant issue is how to combine the spatial KBs with
“ordinary” OWL ontologies. Recently, it has been shown that DL knowledge bases
can be coupled to qualitative spatial KBs using the E -Connections technique
[
E -Connections can also be used for coupling Description Logic KBs together
in a Semantic Web context. In particular, in [
Also recently, it has been shown that RCC-8 KBs can be coupled to DL
KBs using the concrete domain approach [