Completeness proof strategies for Euler diagram logics

James Burton; Gem Stapleton; John Howse

Completeness proof strategies for Euler diagram logics

James Burton
, Gem Stapleton
, John Howse

University of Brighton

Research output: Chapter in Book/Conference proceeding with ISSN or ISBN › Conference contribution with ISSN or ISBN › peer-review

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 language	English
Title of host publication	Euler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams
Place of Publication	Tilburg University, The Netherlands
Publisher	CEUR-WS
Pages	2-16
Number of pages	15
Volume	854
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

Workshop	Euler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams
Period	2/07/12 → …

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Cite this

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title = "Completeness proof strategies for Euler diagram logics",

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.",

author = "James Burton and Gem Stapleton and John Howse",

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year = "2012",

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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, CEUR-WS, Tilburg University, The Netherlands, pp. 2-16, Euler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams, 2/07/12. <http://ceur-ws.org/Vol-854/>

Completeness proof strategies for Euler diagram logics. / Burton, James; Stapleton, Gem; Howse, John.
Euler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams. Vol. 854 Tilburg University, The Netherlands: CEUR-WS, 2012. p. 2-16.

Research output: Chapter in Book/Conference proceeding with ISSN or ISBN › Conference contribution with ISSN or ISBN › peer-review

TY - GEN

T1 - Completeness proof strategies for Euler diagram logics

AU - Burton, James

AU - Stapleton, Gem

AU - Howse, John

PY - 2012/7/2

Y1 - 2012/7/2

N2 - 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.

AB - 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.

M3 - Conference contribution with ISSN or ISBN

VL - 854

SP - 2

EP - 16

BT - Euler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams

PB - CEUR-WS

CY - Tilburg University, The Netherlands

T2 - Euler Diagrams 2012: Proceedings of the 3rd International Workshop on Euler Diagrams

Y2 - 2 July 2012

ER -

Completeness proof strategies for Euler diagram logics

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