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.
|Title of host publication||Euler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams|
|Place of Publication||Tilburg University, The Netherlands|
|Number of pages||15|
|Publication status||Published - 2 Jul 2012|
|Event||Euler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams - Canterbury, UK, 2 July, 2012|
Duration: 2 Jul 2012 → …
|Workshop||Euler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams|
|Period||2/07/12 → …|
Bibliographical note© 2012 for the individual papers by the papers' authors. Copying permitted only for private and academic purposes.
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/