Enhancing the expressiveness of spider diagram systems

Many visual languages based on Euler diagrams have emerged for expressing relationships between sets. The expressive power of these languages varies, but the majority are monadic and some include equality. Spider diagrams are one such language, being equivalent in expressive power to monadic first order logic with equality. Spiders are used to represent the existence of elements or specific individuals and distinct spiders represent distinct elements. Logical connectives are used to join diagrams, increasing the expressiveness of the language. Spider diagrams that do not incorporate logical connectives are called unitary diagrams. In this paper we explore generalizations of the spider diagram system. We consider the effects of these generalizations on the expressiveness of unitary spider diagrams and on conciseness.