Semantics of visual languages

The effective use of visual languages requires a precise understanding of their meaning. Moreover it is impossible to prove properties of visual languages like soundness of transformation rules or correctness results without having a formal language definition. Although this sounds obvious, it is surprising that only little work has been done about the semantics of visual languages, and even worse, there is no general framework available for the semantics specification of different visual languages. The author presents such a framework that is based on a rather general notion of abstract visual syntax. This framework allows a logical as well as a denotational approach to visual semantics, and it facilitates the formal reasoning about visual languages and their properties. He illustrates the concepts of the proposed approach by defining abstract syntax and semantics for the visual languages VEX, Show and Tell, and Euler Circles. For the latter he also proves a rule for visual reasoning.