Dynamic bracketing and discourse representation
type: Item
instance of: scholarly article
title: Dynamic bracketing and discourse representation
zbMATH Open document ID: 0968.03032
author: Albert Visser
author: Kees Vermeulen
published in: Notre Dame Journal of Formal Logic
publication date: 2001-09-11T00:00:00Z
review text: The main idea of this interesting paper is that interpretation of text is a process which produces the meaning. This leads to ``dynamic bracketing'': a sentence is written with brackets, so that `(' opens a new file for storing the subsequent information, and the corresponding `)' closes that file. The simplest structure for stacking cells (fragments) of the text is a monoid. However, monoids are not sufficient for more complex structures, where cells can be stacked at different levels. For this purpose the paper uses m-categories, which are similar to monoidal categories. An essential mechanism is the Grothendieck construction, yielding a category of pairs \((a,t)\), where \(a\) is an object of some m-category \({\mathbf A}\), \(t\) is an object of \(\Theta(a)\), where \(\Theta\) is a given functor from \({\mathbf A}\) to the category of all m-categories. Here \({\mathbf A}\) is understood as a category of contexts, \(\Theta(a)\) as the category of contexts above \(a\). The Grothendieck construction allows to describe various phenomena in text interpretation, such as dynamic quantifiers [\textit{J. Groenendijk} and \textit{M. Stokhof}, Linguist. Philos. 14, 39-100 (1991; Zbl 0726.03024); \textit{C. F. M. Vermeulen}, J. Log. Lang. Inf. 2, 217-254 (1993; Zbl 0802.03024)] or use of pronouns.
Mathematics Subject Classification ID: 03B65
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 91F20
zbMATH DE Number: 944262
zbMATH Keywords: sentence structure
zbMATH Keywords: text structure
zbMATH Keywords: meaning
zbMATH Keywords: dynamic brackets
zbMATH Keywords: stacking cells
zbMATH Keywords: monoid
zbMATH Keywords: m-category
zbMATH Keywords: Grothendieck construction
reviewed by: Valentin Shehtman
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1040046091
OpenAlex ID: W1975381796
cites work: Q3997112
cites work: Dynamic predicate logic
cites work: Counting variables in a dynamic setting
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cites work: Q4693151
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cites work: Defaults in update semantics
cites work: Merging without mystery or: Variables in dynamics semantics
cites work: Sequence semantics for dynamic predicate logic
DOI: 10.1305/NDJFL/1040046091
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description: scientific article; zbMATH DE number 944262