Completeness proof strategies for Euler diagram logics

James Burton, Gem Stapleton, John Howse

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

Abstract

Visual logics based on Euler diagrams have recently been developed, including generalized constraint diagrams and concept dia- grams. Establishing the metatheories of these logics includes providing completeness proofs where possible. Completeness has been established for such logics, including Euler diagrams, spider diagrams and a fragment of the constraint diagram logic. In this paper, we identify commonality in their completeness proof strategies, showing how, as expressiveness in- creases, the strategy readily extends. We identify a fragment of concept diagrams and demonstrate that the completeness proof strategy does not extend to this fragment. Thus, we have established that the existing completeness proof strategies are limited. Consequently, we examine the challenge of devising new approaches to proving completeness in more expressive logics.
Original languageEnglish
Title of host publicationEuler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams
Place of PublicationTilburg University, The Netherlands
PublisherCEUR-WS
Pages2-16
Number of pages15
Volume854
Publication statusPublished - 2 Jul 2012
EventEuler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams - Canterbury, UK, 2 July, 2012
Duration: 2 Jul 2012 → …

Workshop

WorkshopEuler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams
Period2/07/12 → …

Bibliographical note

© 2012 for the individual papers by the papers' authors. Copying permitted only for private and academic purposes.

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    Burton, J., Stapleton, G., & Howse, J. (2012). Completeness proof strategies for Euler diagram logics. In Euler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams (Vol. 854, pp. 2-16). CEUR-WS. http://ceur-ws.org/Vol-854/