We can extend this account of meaning to other parts of speech, and show how the semantic values of larger constituents are built up compositionally from the semantic values of their sub-constituents. Think back to our discussion, in chapter 3, of the MSBLOCKS program, and in particular the set of unchangeable facts about the blocks-world:
[boxB isa box] [boxB size large] [boxB colour blue]
[boxb isa box] [boxb size small] [boxb colour blue]
[boxR isa box] [boxR size large] [boxR colour red]
[boxr isa box] [boxr size small] [boxr colour red]
[boxG isa box] [boxG size large] [boxG colour green]
[boxg isa box] [boxg size small] [boxg colour green]
The meaning of the noun `box' is simply the relevant set of descriptions in the database, and its extension the set of individuals denoted by ?box when the pattern [?box isa box] is matched against the database. For the database above, these are the objects denoted by boxB, boxb, boxR, boxr, boxG, and boxg. What about the meaning of, say, `small'? This is simply the set of descriptions picking out all individuals in the world that are small, in this case the objects denoted by boxb, boxr, and boxg. In the same way, the meaning of `red' is the set of descriptions which identify all individuals whose colour is red: those represented by boxR and boxr. We are now in a position to work out the meaning of a noun-phrase like `small red box', and we do so according to the rule-by-rule principle by which we build up the semantic value of a phrase in tandem with its syntactic parse. The parse and semantic value for `box' is shown in figure 5.6.
We now build up the noun-phrase, such that the database facts about `red' reduce the number of candidates (see figure 5.7). Finally, for the whole noun-phrase, the set of candidates is reduced further (see figure 5.8).
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Figure 5.6: The parse and semantic value for `box'.
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Figure 5.7: The parse and semantic value for `red box'.
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Figure 5.8: The parse and semantic value for `small red box'.
The meaning of `small red box' is the description, or internal representation, which identifies that item which is at the same time a box, red, and small, or in other words the extension of ?box for the database query produced by the parse
[?box size small] [?box colour red] [?box isa box]
That object is the box denoted by boxr. An alternative way of representing this fact is as the intersection of the three sets (see figure 5.9).
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Figure 5.9: A set representation of meaning.
One problem is what to do when there is more than one object known to the database that satisfies all of the conditions contained in a database query. For example, there may be more than one small red box (or another gallery in London which sits in a square containing a monument). One way of dealing with this type of indeterminacy is to look at the determiner of the top-level noun-phrase. If it is `a' or `an', as in ``Is there a small red box on the table?'' then the questioner is indicating that any small red box would be satisfactory. Similarly, the question ``Is there a gallery near here?'' indicates that the questioner will be happy with any nearby gallery (the questioner simply wants a day out looking at pictures) and any of the items that match the database query will be sufficient. On the other hand, if the determiner is `the', then the questioner probably had a particular small red box (or gallery) in mind, and if there is more than one that could be referred to, the questioner should be asked which one is meant. This is not a problem we shall discuss further; in all our examples where we use the definite article `the', there will be a unique object that satisfies the description.
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