Fragments of Spider Diagrams of Order and Their Relative Expressiveness

Abstract. Investigating the expressiveness of a diagrammatic logic provides insight into how its syntactic elements interact at the semantic level. Moreover, it allows for comparisons with other notations. Various expressiveness results for diagrammatic logics are known, such as the theorem that Shin's Venn-II system is equivalent to monadic first order logic. The techniques employed by Shin for Venn-II were adapted to allow the expressiveness of Euler diagrams to be investigated. We consider the expressiveness of spider diagrams of order (SDoO), which extend spider diagrams by including syntax that provides ordering information between elements. Fragments of SDoO are created by systematically removing each aspect of the syntax. We establish the relative expressiveness of the various fragments. In particular, one result establishes that spiders are syntactic sugar in any fragment that contains order, negation and shading. We also show that shading is syntactic sugar in any fragmen...

• Type: Conference
• Year: 2010
• Where: DIAGRAMS
• Authors: Aidan Delaney, Gem Stapleton, John Taylor, Simon J. Thompson
• Keywords: Artificial Intelligence, Diagrammatic Logics, DIAGRAMS 2010, Logic, Spiders