A Logic-based Formalism for Reasoning about Visual Representations (Extended Abstract)

This paper presents a logic-based formalism for formal reasoning about visual representations. This formalism is based on previous work about describing visual notations (Haarslev 1998). However, in this paper we discuss major extensions to this formalism providing decidable reasoning mechanisms that support truly spatial domains such as geographical information systems (GIS). We sketch out the application of this formalism to the specification of syntax and semantics of visual query languages for GIS and to meta reasoning about spatial queries. Our logic formalism integrates research from the AI community ·-especially description logic and constraint solvingand from the qualitative spatial reasoning community. It can be considered 3.':i a decidable formalism for spatial knowledge representation. We think that our formalism is well suited to handle truly visual representations, i.e. representations that exploit geometric or depictional constraints permitted by the plane. The above-mentioned domain of visual spatial query languages for GIS is a suitable candidate for exhibiting truly visual representations. Our formalism is based on a recently developed description logic (DL) offering mechanisms for integrating so-called concrete domains (Ivloller, Haarslev, & Lutz 1997; Lutz, Haarslev, & Moller 1997; Haarslev, Lutz, & Moller 1998b) . We already explored suitable candidates for concrete domains that are based on theories about qualitative spatial reasoning (e.g. Egenhofer's work (Egenhofer 1991) or RCC8 (Randell, Cui , & Cohn 1992)) or about time (e.g. Allen 's interval logic (Allen 1983)) . These findings are also relevant for visual languages (VL) theory since they can provide a basis for specifying visual procedural semantics (time) or for specifying qualitative and quantitative (e.g. geometric) relationships about space. However, in this paper we only focus on spatial reasoning about visual representations. In our earlier work (Haarslev 1995; Haarslev & Wessel 1996; Haarslev 1998) spatial relations (e.g. touching, containing, etc.) are considered as un interpreted (primitive) binary relations with respect to DL theory. In order to correctly deal with spatial objects we needed an exter-