Interpreting Language with Continuation-Based Semantics

Abstract

Starting with Montague’s lambda calculus for explaining natural language, programming language and natural language have had many commonalities that allowed theories in one to explicate phenomena in the other. In this thesis, we examine continuation passing style, a style of writing code that was first developed in programming languages. In continuation passing style, every expression is defined in relation to its "continuation", or the program that follows after it. This style of programming makes the control of the program and its ordering explicit when it may not be the case otherwise. In this thesis, we explore an application of continuations and continuation passing style to natural language. Continuation-based semantics is a theory of explaining natural language that defines pronouns and quantifiers the way that continuations are defined in programming languages. This thesis considers continuation-based semantics as a theory that can potentially explain the phenomenon of crossover evaluation in natural language. We first begin by examining the operators used in continuation-based semantics to distinguish the role of quantifiers and pronouns in ambiguous sentences. Then, in order to better understand continuation-based semantics, we build a parser and interpreter based on rules that we have identified. We then use the parser and interpreter to examine how continuation-based semantics handles a range of ambiguous sentences and sentences that require crossover evaluation. We found that continuation-based semantics can successfully handle sentences that are ambiguous because of how quantifier scope or quantifier binding applies. In terms of crossover evaluation, we found that while continuation-based semantics can handle more instances of crossover evaluation in comparison to traditional theories of semantics, it still does not work in some natural language cases that require a crossover evaluation interpretation.