The systematic design of visual languages applied to logical reasoning

Visual languages are distinguished by a number of graphical objects and their relations, usually arranged in the two-dimensional plane. While objects and relations are syntactical containers which are used to represent some information, the question arises how to systematically treat all possible syntactical containers given the richness and complexity of the underlying geometry. This paper adopts the intersection paradigm applied in the context of spatial reasoning, which ensures the systematic identification of all conceivable well-formed diagrams. This allows the exhaustive analysis of a visual language. As an example, it is shown how this method enables a thorough understanding of the relations of the graphical elements of linear diagrams which represent monadic first-order logic. The consideration of indeterminate sets even demonstrates the effectiveness of this approach for a representation that includes a total of 512 relations.