3 Scope and Underspecification

In the previous lecture, we have seen how we can compute semantic representations for simple sentences. The formal tool we have used for this purpose was -calculus, and the linguistic theory we have followed was Montague Semantics.

Now of course Montague Semantics does not cover all semantic phenomena there are; otherwise semanticists would be out of jobs by now. The good news, however, is that the insights into the structure of semantic representations that Montague gained are so fundamental that many modern semantic theories still uphold Montague Semantics when dealing with simple sentences. Such theories typically come with extensions to the formal framework to allow them the necessary flexibility.

In this lecture, we will investigate the classical case in which Montague Semantics fails to compute the correct meaning(s): scope ambiguities, a certain kind of semantic ambiguity. In the first part, we talk about what scope ambiguities are and why the mechanisms we know so far aren't powerful enough to compute them. In the second part of the lecture we learn about a rather modern approach to dealing with scope, based on underspecification with dominance constraints [EKN01]. Finally, we look at the computational problems connected to this approach and show how to solve them - first in an abstract way and then (in the next Chapter) by means of a Prolog implementation.

• 3.1 Scope Ambiguities
  • 3.1.1 What Are Scope Ambiguities?
  • 3.1.2 Scope Ambiguities and Montague Semantics
  • 3.1.3 A More Complex Example
  • 3.1.4 The Fifth Reading
  • 3.1.5 Montague's Approach to the Scope Problem
  • 3.1.6 Quantifying In: An Example
  • 3.1.7 Other Traditional Solutions
  • 3.1.8 The Problem with the Traditional Approaches

• 3.2 Underspecification
  • 3.2.1 Introduction
  • 3.2.2 Computational Advantages
  • 3.2.3 Underspecified Descriptions
  • 3.2.4 The Masterplan
  • 3.2.5 Formulas are trees!
  • 3.2.6 Describing Lambda-Structures
  • 3.2.7 From Lambda-Expressions to an Underspecified Description
  • 3.2.8 Relating Constraint Graphs and Lambda-Structures
  • 3.2.9 Sidetrack: Constraint Graphs - The True Story
  • 3.2.10 Sidetrack: Predicates versus Functions