A Fully Formalized Theory for Describing Visual Notations

Abstract

This paper addresses issues in visual language theory with the help of logic formalisms that were developed for reasoning tasks by the artificial intelligence and spatial databases community, especially for spatial and diagrammatical reasoning. We describe an approach based on three formal components. Topology is used to define basic geometric objects. Theory about spatial relations from the domain of spatial databases is employed to define possible relationships between visual language elements. Description logic theory from the AI community is used to combine topology and spatial relations. The resulting theory has been successfully applied to formally specifying semantics of visual languages. The theory's application is illustrated with a specification of entity-relationship diagrams.

GenEd-an editor with generic semantics for formal reasoning about visual notations

“…That is, the meanings of represented language concepts should be unambiguously determined by explicit notational formalisms, so that algorithms can operate on the representation in accordance with the semantics of the notation, without needing ad hoc provisions for specific VL domains. Our approach is based on a fully formalized theory [4] for describing visual notations that consists of three components. Each component is defined by precise semantics.…”

“…In contrast to several other approaches for spatial relations (e.g. see [4]) GenEd can also deal with concave objects. Additionally, an arbitrary collection of objects may be grouped together and treated as a composition object.…”

“…[19,20,21,22,23,24,25]) for representing spatial relationships. A more detailed review of closely related work on VL theory can be found in [4].…”

“…We are planning to incorporate concrete domains over the algebra of simple reals. These concrete domains extend description logic by reasoning about systems of (in)equalities over (non)linear polynomials (see [4] for more details). We also plan to address dynamic semantics of VLs.…”

“…It also introduces a new full-featured graphic editor based on our formal theory. This theory was introduced in [1] and is extensively presented and related to visual language theory in [4]. Our approach is in contrast to other approaches that use only syntax specifications or favor a generative solution, i.e.…”