Lexicalisation of montague semantics: a unified approach to semantic interpretation

Abstract

This thesis presents the X/LTAG model, a novel framework for semantic representation that integrates the Lexicalized Tree Adjoining Grammar (LTAG) formalism of Arvind Joshi with the possible world semantics of Richard Montague. The X/LTAG model is designed to be compositional and employs a uniform semantic object structure, offering advantages over existing models of semantic interpretation. It maintains mild context sensitivity to ensure observational adequacy for complex linguistic phenomena. At the core of the model is the X/LTAG tree set, which provides primitive semantic units used to construct elementary trees. These trees are equivalent to LTAG elementary trees and encode the semantics of their lexical anchors using intensional logic expressions. A parsing algorithm is developed to construct semantic objects alongside syntactic trees, supporting adjunction and substitution operations uniformly. The model effectively addresses quantifier scope issues by using a single generic semantic object, represented as a tree with nodal semantics. Despite its strengths, the X/LTAG model faces challenges when implemented with standard models of interpretation, such as computational saturation due to the exponential growth of denotations. Additionally, ambiguity in denotations - such as word sense and structural ambiguity - remains unresolved formally, though practical systems often rely on heuristic approaches. Overall, the X/LTAG model offers a formal and general foundation for semantic interpretation in natural language processing, bridging gaps between syntactic advances and semantic theory.