Dynamic bracketing and discourse representation
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.
scientific article; zbMATH DE number 944262