5.2.4 The Masterplan
Plan for the rest of the chapter.
In order to give underspecified descriptions of possible readings, the first thing we need is a way of talking about the structure of formulas and of
-expressions. We will represent formulas and
Then (in Section 5.2.6) we will introduce a formalism that allows us to describe trees (and thereby formulas and
Once we know how an underspecified description describes (one or more) tree representations of
In the rest of this chapter and in the next one, we will go into the details of underspecification. What exactly are we going to do? We will first give you an intuition of what the formalism to be presented does, and then make this intuition more formal. Here's how we will proceed:
In order to give underspecified descriptions of possible readings, the first thing we need is a way of talking about the structure of formulas and of
-expressions. We will represent formulas and -expressions as trees. So to begin with (Section 5.2.5), we'll explain how to do this.Then (in Section 5.2.6) we will introduce a formalism that allows us to describe trees (and thereby formulas and
-expressions). This formalism is called normal dominance constraint s. As a concrete example, we will look at the two -expressions (written as trees!) for our running example ``Every man loves a woman'' (Section 5.2.7) and see how we can represent them using only one underspecified description from our new formalism. We will learn how we can construct this description from the two -expressions.Once we know how an underspecified description describes (one or more) tree representations of
-expressions, we turn to the question that's most important when we build semantic representations for a sentence: How do we solve underspecified descriptions? That is, given an underspecified description, how can we compute the formulae it describes? In our formalism of normal dominance constraints, this involves a process called constraint solving . In the rest of this chapter we will give you a first intuition of what the problem is that we have to deal with (Section 5.2.8). In the next chapter, we will then continue our discussion by formulating an algorithm that incorporates this intuition. Section 6.1 introduces the basic concepts used in that algorithm. In Section 6.2 we consider one by one each of its subtasks.
Below you see again the general picture of underspecification-based semantic construction that you know from Section 5.2.1. But this time we've marked in blue what we will have dealt with when we're through with the three points just mentioned. Additionally we've filled in the boxes with the types of representation we're actually going to use:
Now you probably wonder: Isn't there something missing? What about the grey part of the picture above? We plan to discuss at length how underspecified descriptions relate to formulas, and even give an algorithm that constructs the latter from the former. But we seem to keep secret how to get from natural language sentences to underspecified descriptions...
You are right with this observation! At that stage we will not yet know how to construct e.g the one underspecified description of the two readings of ``Every man loves a woman'' from this sentence. And of course we have to know how to do this. Yet we will not bother about this task until the very end of the next chapter (Section 6.4), when we actually implement semantic construction based on our underspecification formalism.
The reason for this postponement is that the actual construction of underspecified descriptions from sentences is by far the easiest step in our new semantic construction system. It's less complicated than the subsequent step of constraint solving, and it's even less complicated than the direct construction of -expressions that we're used to from our Montague based approach.