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1	Plurality and quantification in graph representation of meaning
	Cao, Yu (author); Charlow, Simon (chair); Jardine, Adam (member); Tesar, Bruce (member); Pietroski, Paul (member); Barker, Chris (member); Rutgers University; School of Graduate Studies. - 2021
	Abstract: The study of meaning is inseparable from that of semantic representation, as design efforts in the latter exert far-reaching implications for linguistics and related computation. In this thesis, we present a representation formalism based on directed graphs and explore its explanatory benefits in application to classic issues in plurality and quantification, two aspects of natural language semantics treated in previous graph formalisms with varied linguistic adequacy. Our graph language (Chapter 2) covers the essentials of natural language semantics (thematic relations, modification, co-reference, intensionality, plurality, quantification, and coordination) while using only monadic second-order variables. We show that the model-theoretical interpretation of this language can be defined in terms of graph traversal, where the relative scope of variables arises from their order of valuation. We present a unification-based mechanism for constructing semantic graphs at a simple syntax-semantics interface (Chapter 3), whose task is to decide equivalence among discourse referents introduced by linguistic tokens, through syntax and through non-syntactic resolutions. Syntax is then formulated as a deterministic partition function on discourse referents. By establishing a partly deterministic relation between semantics and syntactic distribution, we show that this function finds a natural implementation in categorial grammars, owing to the way they manipulate syntactic resources. The syntax-semantics interface described here is automated to facilitate future exploration. In applying the present graph formalism to selected topics in plurality and quantification (Chapters 4-5), we show that distributive predication of various forms (and even lack thereof) can be attributed to variants of a graph motif that performs quantification, and the partial determinism between semantics and syntactic distribution allows these variants to share roughly the same syntax. Our syntax-semantics interface offers streamlined solutions to compositional problems in cross-categorial conjunction and scope permutation of quantificational expressions. A scope taking strategy analogous to co-reference resolution is shown to simplify the treatment of exceptional scoping behaviors of indefinites. ; Ph.D. ; Includes bibliographical references
	Keyword: graph; Linguistics; plurality; quantification; semantic representation
	URL: http://dissertations.umi.com/gsnb.rutgers:11601
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