5.2.1 Introduction

Introduction of underspecification.

A Clean and Declarative Approach

So basically, we are going to separate semantic construction from the enumeration of readings of ambiguities. We thus divide the problem into two independent parts, which we can in turn solve independently. This means we can stick to our original setup, where we derive one representation from one syntactic analysis, only now this representation is the description of a whole set of readings. It also means we can take a more declarative perspective on scope ambiguity: First of all, we specify what readings a sentence should have, and in a second step we can think about how to actually compute them. We call this step of enumerating the single readings solving. Our algorithm for this task will turn out to be quite an elegant one, constituting a great step forward from traditional Cooper or Hobbs style algorithms, which not only had to think about the structure of the semantics, but also about syntactic considerations.

Let us now sum up our discussion so far, using a few pictures. Then we illustrate how our new underspecification based approach relates to the Montague style semantic construction system from the last chapters, and to its extensions that we discussed in the first part of this chapter.

Here's a schema of how we get from a sentence to its semantic representation in the standard case that our Montague style system covers: Unambiguous sentences like ``John loves Mary''.

Standard Montague

We've discussed a much more detailed version of this picture in the last chapter- the semantic representation of the sentence is constructed via and along with its syntactic analysis. One syntactic analysis can only yield one semantic representation. Now since we've assumed that our input sentence is unambiguous, that's fine. There is in fact only one semantic representation for it.

But as we have seen in the first sections of this chapter, there are sentences that contain genuinely semantic ambiguities. The paradigmatic case we've looked at is that of quantifier scope ambiguities as in ``Every man loves a woman''. The following graphic depicts the situation when we feed that sentence to our Montague style semantic construction system:

The Problem

There are two semantic representations that should be associated with our input sentence, due to the scope ambiguity in it. But our system can only construct one of them. That's because there's only one syntactic analysis for the sentence, and as we've just mentioned, one syntactic analysis can only yield one semantic representation.

So if we don't want to change anything substantial in the approach we've implemented, there seems to be only one way to get to the second reading. That is to allow a second syntactic analysis.

Montague with Quantifying In

Now we would be able to construct the second semantic representation together with this second syntactic analysis. As we've said (in Section 5.1.5), this is the solution that Montague himself adopted. But we've also discussed that there's one strong and obvious argument against this solution: Scope ambiguities simply are not syntactic. According to our intuitions, our example sentence is syntactically unambiguous, and so we should not for purely technical reasons claim the opposite.

Underspecification allows for a more satifactory solution to our problem:

Underspecification

We have split the ``semantic side'' of our picture in two levels. On one level we have underspecified descriptions, and on the other one the semantic representations we're used to (i.e. -expressions and - at the end of the day - first order formulae). With this two-leveled architecture we can again construct one underspecified description along with only one syntactic analysis. But this one underspecified description sometimes describes many readings on the level of -expressions. This means that we have now captured the semantic ambiguity in truly semantic terms. Our first-level semantic representation (the underspecified description) remains ambiguous between multiple second-level semantic representations (-expressions) in the same way as the original sentence.

Terminology

Before we go on, let us sort out our terminology a bit. Up to now, we've used the term ``semantic construction'' to denote the whole business of getting from natural language sentences to first order formulas. From now on, we will often have to differentiate a bit more. We will then use ``semantic construction'' in a more narrow sense, only for the way from natural language sentences to underspecified descriptions. We will call the step from underspecified descriptions to -expressions solving.

As regards the term ``semantic representation'', we'll sometimes use it as an umbrella term for underspecified descriptions as well as -expressions and first order formulas. But whenever it is important, we will carefully distinguish between the three.