Claudia Anger

The Region Connection Calculus (RCC) is a qualitative spatial reasoning formalism, developed in knowledge representation and geographical information systems. We argue that RCC can be viewed as a more fine-grained approach to the use of Euler diagrams to visualize categorical statements like ‘all A are B’. We present RCC using the syntax of first-order modal logic and a topological semantics. We compare the Gergonne relations (a well-known set of 5 jointly exhaustive and pairwise disjoint relations between two non-empty sets, visualized using Euler-type diagrams) with RCC8 (a similar set of 8 relations for regions).

In the vein of a renewed interest in diagrammatic reasoning, this paper challenges an opposition between logic diagrams and formal languages that has traditionally been the common view in philosophy of logic and linguistics. We examine, from a philosophical point of view, what we call five dogmas of logic diagrams. These are as follows: (1) diagrams are non-linguistic; (2) diagrams are visual representations; (3) diagrams are iconic, and not symbolic; (4) diagrams are non-linear; (5) diagrams are heterogenous, and not homogenous. Using historical examples, we argue that none of these dogmas is an adequate criterion to distinguish logic diagrams from formal languages. Instead, we advocate that there is a common core between linguistic and diagrammatic representation and reasoning.