7.1.7 Natural Language Semantics

Bringing together logics and NLP.

Let us now relate all of this to what we've learned so far about natural language semantics. Our overall aim is to develop a set of methods to determine the meaning of natural language. If we look back, all we did was semantic construction. We established translations from natural languages into formal languages like first-order logic (and that is all you will find in most semantics papers and textbooks). Now, we have just tried to convince you that formulae of these formal languages are themselves again nothing but syntactic entities that can be processed on syntactic grounds in calculi. So, where is the semantics? In fact, we have got it once we have a correct and complete calculus.

Why is this true? Basically, our argument goes as follows: The semantics of a sentence is reflected in what follows from it. The translation methods we already have give us first-order logical formulas for sentences. Now we said above that we take the logical consequence relation between such first-order formulae as a simplified version of the ``follows from'' relation between the sentences they translate. Now, a complete and correct calculus captures this logical consequence relation between formulae - in terms of their syntax. So it also captures the ``follows from'' relation between the corresponding sentences, and thus their semantics, in syntactic terms.

Let us consider the following diagram to shed more light on this situation:

As we mentioned, the green area is the one generally covered by natural language semantics (and all that we covered in the preceding chapters). In the semantics construction process, the natural language utterances (viewed here as ``formulae'' of a language ) are translated to a formal language (in our case first-order logic). Now the argument given above shows that this is all that is needed to recapture the semantics of . Even though it is not immediately obvious at first: Theoretical logic gives us the missing pieces.

Let us reformulate our argument in the terminology used in the diagram. Since is a formal language of a logical system, it comes with a notion of model and an interpretation function that translates formulae into objects of such models. Models induce a notion of logical consequence1 as explained in Section 1.1.2. The formal language also comes with a calculus acting on -formulae, which (if we are lucky) is correct and complete (then the mappings in the upper rectangle commute2).

In natural language semantics we are interested in ``follows from'' relations on natural language utterances, which we have denoted by . If the calculus of the logic is correct and complete, then it is a model of the relation . In this case we really have a formal handle on the ``follows from'' relation for natural language utterances if we only specify our semantics construction (the green part) method and the matching calculus.


1. Relations on a set are subsets of the Cartesian product of , so we use to signify that is a ( -ary) relation.
2. We say that arrows in a diagram commute, if we can compose the mappings on any path and always arrive at the same result.

Aljoscha Burchardt, Stephan Walter, Alexander Koller, Michael Kohlhase, Patrick Blackburn and Johan Bos
Version 1.2.5 (20030212)