Spider Diagrams of Order and a Hierarchy of Star-Free Regular Languages

Abstract. The spider diagram logic forms a fragment of constraint diagram logic and is designed to be primarily used as a diagrammatic software specification tool. Our interest is in using the logical basis of spider diagrams and the existing known equivalences between certain logics, formal language theory classes and some automata to inform the development of diagrammatic logic. Such developments could have many advantages, one of which would be aiding software engineers who are familiar with formal languages and automata to more intuitively understand diagrammatic logics. In this paper we consider relationships between spider diagrams of order (an extension of spider diagrams) and the star-free subset of regular languages. We extend the concept of the language of a spider diagram to encompass languages over arbitrary alphabets. Furthermore, the product of spider diagrams is introduced. This operator is the diagrammatic analogue of language concatenation. We establish that star-free ...

• Type: Conference
• Year: 2008
• Where: DIAGRAMS
• Authors: Aidan Delaney, John Taylor, Simon J. Thompson
• Keywords: Artificial Intelligence, Diagrammatic, Diagrammatic Logics, DIAGRAMS 2008, Spider Diagrams