MoL-2014-14: An Automata-Theoretic Perspective on Polyadic Quantification in Natural Language

MoL-2014-14: McWhirter, Sarah (2014) An Automata-Theoretic Perspective on Polyadic Quantification in Natural Language. [Report]

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Abstract

As part of the general project of procedural semantics, nearly thirty years ago van Benthem first proposed semantic automata as a computational model of natural language quantification. While automata-theoretic characterization results have been obtained for monadic quantifiers, very little has been done to investigate polyadic quantifiers from this perspective. Polyadic quantification in natural language includes but is not limited to iteration, cumulation, resumption, reciprocals, and branching. A natural extension of the semantic automata model is to study the properties of automata recognizing polyadic quantifiers, and the operations on simple automata corresponding to the lifts giving rise to them.
The thesis gives automata constructions for iteration and cumulation and answers (affirmatively) the open question of whether deterministic PDA are closed under these operations. These efforts pave the way toward a novel understanding of the closely related Frege boundary between reducible and ~genuinely polyadic~ quantification (studied by van Benthem, Keenan, Dekker, and van Eijck, among others) in automata-theoretic terms. An extension of semantic automata for the polyadic lifts which are largely non-Fregean in this sense is left for future work. Finally, the thesis concludes with discussion of the applications of our results and reflection on the importance of representations to the further advancement of this paradigm.

Item Type:	Report
Report Nr:	MoL-2014-14
Series Name:	Master of Logic Thesis (MoL) Series
Year:	2014
Uncontrolled Keywords:	logic, language
Subjects:	Logic
Date Deposited:	12 Oct 2016 14:38
Last Modified:	12 Oct 2016 14:38
URI:	https://eprints.illc.uva.nl/id/eprint/932

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