Generalizing spiders

Gem Stapleton, John Howse, Kate Toller

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNConference contribution with ISSN or ISBN

Abstract

Recent times have seen various formal diagrammatic logics and reasoning systems emerging [1, 4, 5, 7]. Many of these logics are based on the popular and intuitive Euler diagrams; see [6] for an overview. The diagrams in figure 1 are all based on Euler diagrams and are examples of unitary diagrams. Compound diagrams are formed by joining unitary diagrams using connectives such as ‘or’. We generalize the syntax of spider diagrams (of which d 3 in figure 1 is an example), increasing the expressiveness of the unitary system. These generalizations give rise to a more natural way of expressing some statements because there is an explicit mapping from the statement to a generalized diagram. Our theoretical motivation is to provide the necessary underpinning required to develop efficient automated theorem proving techniques: developing such techniques for compound systems is challenging and enhancing the expressiveness of unitary diagrams will enable more theorems to be proved efficiently.
Original languageEnglish
Title of host publicationProceedings of the 4th International Conference, Diagrams 2006
Place of PublicationBerlin Heidelberg
PublisherSpringer
Pages148-150
Number of pages3
Volume4045
ISBN (Electronic)9783540356240
ISBN (Print)9783540356233
DOIs
Publication statusPublished - 1 Jan 2006
EventProceedings of the 4th International Conference, Diagrams 2006 - Stanford, CA, USA, 28-30 June, 2006
Duration: 1 Jan 2006 → …

Publication series

NameLecture Notes in Computer Science

Conference

ConferenceProceedings of the 4th International Conference, Diagrams 2006
Period1/01/06 → …

Bibliographical note

The original publication is available at www.springerlink.com

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    Stapleton, G., Howse, J., & Toller, K. (2006). Generalizing spiders. In Proceedings of the 4th International Conference, Diagrams 2006 (Vol. 4045, pp. 148-150). (Lecture Notes in Computer Science). Springer. https://doi.org/10.1007/11783183_19