On diagram tokens and types

John Howse, Fernando Molina, Sun-Joo Shin, John Taylor

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNConference contribution with ISSN or ISBNResearchpeer-review

Abstract

Rejecting the temptation to make up a list of necessary and sufficient conditions for diagrammatic and sentential systems, we present an important distinction which arises from sentential and diagrammatic features of systems. Importantly, the distinction we will explore in the paper lies at a meta-level. That is, we argue for a major difference in meta-theory between diagrammatic and sentential systems, by showing the necessity of a more fine-grained syntax for a diagrammatic system than for a sentential system. Unlike with sentential systems, a diagrammatic system requires two levels of syntax-token and type. Token-syntax is about particular diagrams instantiated on some physical medium, and type-syntax provides a formal definition with which a concrete representation of a diagram must comply. While these two levels of syntax are closely related, the domains of type-syntax and token-syntax are distinct from each other. Euler diagrams are chosen as a case study to illustrate the following major points of the paper: (i) What kinds of diagrammatic features (as opposed to sentential features) require two different levels of syntax? (ii) What is the relation between these two levels of syntax? (iii) What is the advantage of having a two-tiered syntax?
Original languageEnglish
Title of host publicationProceedings of the Second International Conference, Diagrams 2002
Place of PublicationBerlin Heidelberg
Pages76-90
Number of pages15
Volume2317
ISBN (Electronic)9783540460374
DOIs
Publication statusPublished - 1 Jan 2002
EventProceedings of the Second International Conference, Diagrams 2002 - Callaway Gardens, GA, USA, April 18–20, 2002
Duration: 1 Jan 2002 → …

Publication series

NameLecture Notes in Computer Science

Conference

ConferenceProceedings of the Second International Conference, Diagrams 2002
Period1/01/02 → …

Fingerprint

Syntax
Diagrams
Leonhard Euler
Necessary and Sufficient Conditions
Physical
Temptation
Metatheory

Cite this

Howse, J., Molina, F., Shin, S-J., & Taylor, J. (2002). On diagram tokens and types. In Proceedings of the Second International Conference, Diagrams 2002 (Vol. 2317, pp. 76-90). (Lecture Notes in Computer Science). Berlin Heidelberg. https://doi.org/10.1007/3-540-46037-3_18
Howse, John ; Molina, Fernando ; Shin, Sun-Joo ; Taylor, John. / On diagram tokens and types. Proceedings of the Second International Conference, Diagrams 2002. Vol. 2317 Berlin Heidelberg, 2002. pp. 76-90 (Lecture Notes in Computer Science).
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Howse, J, Molina, F, Shin, S-J & Taylor, J 2002, On diagram tokens and types. in Proceedings of the Second International Conference, Diagrams 2002. vol. 2317, Lecture Notes in Computer Science, Berlin Heidelberg, pp. 76-90, Proceedings of the Second International Conference, Diagrams 2002, 1/01/02. https://doi.org/10.1007/3-540-46037-3_18

On diagram tokens and types. / Howse, John; Molina, Fernando; Shin, Sun-Joo; Taylor, John.

Proceedings of the Second International Conference, Diagrams 2002. Vol. 2317 Berlin Heidelberg, 2002. p. 76-90 (Lecture Notes in Computer Science).

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNConference contribution with ISSN or ISBNResearchpeer-review

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Howse J, Molina F, Shin S-J, Taylor J. On diagram tokens and types. In Proceedings of the Second International Conference, Diagrams 2002. Vol. 2317. Berlin Heidelberg. 2002. p. 76-90. (Lecture Notes in Computer Science). https://doi.org/10.1007/3-540-46037-3_18