Set space diagrams

• Set space diagrams (SSDs) can be more easily constructed than Venn diagrams.
• Usefulness of SSDs derives from relevance of Venn diagrams which are widespread.
• SSDs provide tidy overview on sets and their relations, even for more than four sets.
• Details can be easily verified, such as intersections or containment relations.
• Operations and equations among sets can be easily visualised and verified.

This paper introduces set space diagrams and defines their formal syntax and semantics. Conventional region based diagrams, like Euler circles and Venn diagrams, represent sets and their intersections by means of overlapping regions. By contrast, set space diagrams provide a certain layout that avoids overlapping geometrical entities. This enables the representation of a good deal of sets without getting diagrams which are cluttered due to overlapping regions. In particular, these diagrams can be employed for illustration purposes, e.g., for showing the laws of Boolean algebras. Additionally, cardinalities are represented and can be easily compared; inferences can be drawn to derive unknown cardinalities from a given knowledge base. The soundness of set space diagrams is shown with respect to their set-theoretic interpretation.