Plurality and Quantification in Graph Representation of Meaning

TL;DR

This thesis introduces a graph-based semantic formalism for natural language that models plurality and quantification, offering a unified, automated approach to complex linguistic phenomena like scope and distributive predication.

Contribution

It presents a novel graph language for semantics using monadic second-order variables, with a model-theoretic interpretation and an automated syntax-semantics interface mechanism.

Findings

Successfully models scope permutation of quantifiers

Handles distributive predication and cross-categorial conjunction

Automates semantic graph construction from syntax

Abstract

In this thesis we present a semantic representation formalism based on directed graphs and explore its linguistic adequacy and explanatory benefits in the semantics of plurality and quantification. Our graph language covers the essentials of natural language semantics using only monadic second-order variables. We define its model-theoretical interpretation 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, where syntax as a partition function on discourse referents is implemented with categorial grammars by establishing a partly deterministic relation between semantics and syntactic distribution. This mechanism is automated to facilitate future exploration. The present graph formalism is applied to linguistic issues in distributive predication, cross-categorial conjunction, and scope permutation of quantificational expressions, including the exceptional scoping behaviors of indefinites.