Plurality and Quantification in Graph Representation of Meaning
This work addresses linguistic semantics challenges for researchers in computational linguistics, though it appears incremental as it builds on existing graph and categorial grammar methods.
The thesis tackles the problem of representing natural language semantics for plurality and quantification by introducing a graph-based formalism, achieving a unified approach that handles distributive predication, cross-categorial conjunction, and quantifier scope permutations through automated mechanisms.
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.