next up previous
Next: Theoretical Foundation Up: No Title Previous: No Title


This paper reports on an approach to formalizing visual notations. In contrast to many grammatical approaches dealing primarily with syntactic issues of visual languages (VLs) we propose a spatial logic for describing semantics of visual notations. This logic combines three components (topology, spatial relations, description logic) that are themselves also formally specified with precise semantics. These components were derived from research communities that are related to VL research: reasoning on diagrammatic representations and spatial databases. The goal of this paper is the attempt to intensify the dialogue between these research communities and to ``advertise'' the benefits of this particular view of VL theory. The successful application of our theory to a completely visual language for concurrent logic programming, Pictorial Janus (PJ) [1,2], has been reported elsewhere [3,4]. This experience resulted in the development of an editor for visual notations [5] whose generic semantics are based and controlled by the theory described in this paper.

Our approach is generic in the sense that particular instances can be chosen for the above mentioned components. This process depends on the nature of specific visual notations to be formally specified. For instance, the definition of PJ is mostly based on topological relations between lines, arrows, and convex regions. Therefore, we selected corresponding definitions for primitive geometric objects, an appropriate theory on spatial (topological) relations [6] that can deal with true 1D objects and regions, and a matching description logic. However, we like to emphasize that other visual languages or notations might require different definitions for objects and their possible relationships. In the following section we shortly review alternative instances for spatial relations theory.

Volker Haarslev
Tue Jul 2 13:23:22 MET DST 1996