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Levels of Linguistic Meaning and the Logic of Natural Language

Hans Kamp, IMS, University of Stuttgart

When in the second half of the sixties Montague succeeded in applying the methods of model theory to significant fragments of natural language, this came as a great surprise to the community; until then almost everyone had been convinced that natural languages were far too "organic" and unsystematic to permit analyses of this sort. Montague himself emphasised his diverging opinion by stating that there were no significant differences between natural languages and the languages of formal logic.

In the more than three decades which have passed since then, the main ingredient of Montague's method has come to be accepted as something inevitable: the existence, as part of the "grammar" of any natural language, of a set of semantic interpretation rules operating on syntactic structures of expressions which make it possible to compute the semantics of a complex expression from the semantics of its syntactic constituents. For how could language function without such principles; how could people ever make a novel use of complex expressions of the languages we speak if such interpretation principles weren't part of our linguistic knowledge?

At the same time, however, we have come to see that there are a number of aspects of natural language which seem to set natural languages apart from formal languages - at least from those languages of first and higher order predicate logic which served Montague as paradigms when he started developing his theory.

First, there is the all-pervasive presence of vagueness that we find in natural language. For the problems which vagueness, in all its different forms, presents to the classical semantics of Montague Grammar, there exists in my view still no fully satisfactory solution.

Secondly, as we have knownnow for more than two decades, the semantic form of natural language sentences is wedded to their use in discourse, where they serve to update information. It is rare for a sentence of natural language to express the content it is meant to transmit without remainder. Rather, the sentences that are part of a text or conversation rely on information that may be assumed to be in the addressee's possession already, and they are equipped with various kinds of pointers towards bits of that information. This "dynamic" dimension to natural language is also something that the formal languages which served Montague as examples do not possess. This insight has lead to a quite profound change in our understanding of how the semantics of natural language works. As a consequence, our current conception of the architecture of natural language semantics is importantly different from that of Montague Grammar, technically as well as conceptually.

In recent years my own view of what the dynamic aspect of natural language interpetation entails for the general form of a theory of natural language semantics and pragmatics has undergone a non-trivial modification. Until the early nineties my colleagues at the University of Stuttgart and I had been working with a form of "Discourse Representation Theory" (or DRT, our home-grown variety of dynamic Semantics) which goes back to th origins of DRT in 1980 (and of which there is an extnsive documentation in the book "From Discourse to Logic by Uwe Reyle and myself). This version of the theory has since been replaced by one in which each sentence of a conversation or text is first assigned a "preliminary" representation, which is then, in a second stage of the interpetation process, integrated with the already established representation of the context in which the sentence is being used. There are several compelling reasons for this change. In particular, there is (i) the need for underspecified representations (see Reyle (1993); (ii) the constraints imposed by the treatment of presupposition (Van Der Sandt, 1992); and (iii) more recently, the need to incorporate unification-based principles into the construction of sentence representations.

Among the advantages of this two-stage DRT architecture is that it makes a cluster of further differences between natural languages and the languages of formal logic clearly visible as well. These have to do (i) with the extraordinary complexity of the semantics of lexical items and (ii) (in particular) with the circumstance that so many words of any natural language are ambiguous (indeed, often, multiply ambiguous). Because of this, building the intended semantic representation of a complex natural language expression isn't just a matter of putting its meaning together from the meanings of its lexical constituents. The harder problem, we now realise, is to determine what the right meanings of the lexical constituents are for this particular complex expression, or this particular utterance - the problem, that is, to get rid of all the unwanted meanings of the lexical constituents in the course of computing the intended mening of the whole. In fact it is here, I think, that we see the true magic of natural language semantics: massive ambiguity at the base typically narrows down to an unequivocal semantic value at the top.

The processes needed to arrive at unequivocal interpretations from a highly ambiguous input are complex. They are very much more complex than they would need to be if the right choice of lexical meanings were fixed in advance. For one, these processes seem to involve various kinds of inferencing while the semantic representation is being built; and these inferences usually make use of meaning postulates which capture systematic relations beween different lexical items as well of a wide varierty of world knowledge. The inferences have the effect of transforming semantic representations of one kind into representations of another kind. In fact, it seems likely that two sorts of representation transformations are involved. On the one hand there is transformation of the semantic representations of the sentences or utterances that are geing interpreted. On the other hand we may suspect that at least some of the representations of the world knowledge premises needed in disambiguationhave to be subjected to trnsformation as well. For instance, it has often been suggested that much of the knowledge we acquire through our eyes is stored in the form of "visual" representations. When such visual information is to be combined with the "propositional" representations that are built in the process of interpretation, it has to be turned into a form that is compatible with these propositional representations.

In the talk I will present a few examples to illustrate what mechanisms may be involved in computing the intended interpretation of an utterance. These will provide a glimpse of the data structures which are needed in such computations and the resources of lexical and encyclopaedic knowledge which support them.

This emerging picture of a multiplicity of different forms of information representation suggests a conception of logic that is very different from the one that was prevalent in the early days of Montague Grammar, and, in fact which is still the view espoused by many today. First, different modes of representation each come with their own logic - a different representational syntax requires a different model-theoretic semantics and different forms of inference rules. Secondly, because inference is needed in the course of computing the interpretations of utterances (and not just when the completed interpretation is employed as a premise in subsequent reasoning), inferential principles become part of more general systems of representation transformation, and thus of a general theory of information. To the extent that I can judge, it is this general insight which has driven much of the research carried out within the Spinoza project and, more generally, by the community within which the project has been embedded.)

So far, all this has had to do with linguistic knowledge as we must suppose it to be available to any competent speaker of a natural language. It is the task of linguistics to describe this knowledge. Its explanandum is the observable behaviour of the language users. That observable behaviour is taken to include, first and foremost, the judgements about grammatical correctness and conditions of truth and reference in which their knowledge becomes manifest in particularly direct and telling ways. But is there anything else? It is one of the central methodological questions of linguistics what more might or should be included within its explananda: What besides judgements about wellformedness and meaning should we take to be the linguistically relevant aspects of human behaviour involving language; and furthermore, is here anything beyond linguistic "behaviour" that linguistic theory should account for?

Like other scientific disciplines, linguistics seems to function and thrive well enough without paying too much attention to questions of general methodology. Its case, however, is arguably quite special. On the one hand linguists find themselves confronted with the question whether or not their theories should pay atention to the intersubjective aspects of verbal communication, or to how much of it. Indeed, many of the more fundamental questions of pragmatics seem to turn on such issues. On the other hand there is the question how much attention should linguistics should pay to the subconscious dimension of language processing - that complex of mental processes that are inaccessible to introspection by the language users themselves but of which more and more is getting revealed by the increasingly sophisticated methods of experimental psychology. This is the question about the relationship between linguistics and psycholinguistics. One form in which this question can be asked: Should psycholinguistics be seen as a part of general linguistics, or should we see them as genuinely disctinct disciplines, with linguistics providing the structurl data which psycholingsitics is to account for on the deeper level of actual mental processing?

This last question is one to which different linguists will be inclined to give different answers. But beyond it there looms another one of a similar sort, but far more controversial yet: What if anyting should linguitics have to say about the neurophysiological substratum of linguistic knowledge and the mental processes that are involved in language use? How is linguistic knowledge represented at the neural level? What do our neurons do when we produce an utterance, or hear/read and interpret one? And so on.

From the neural perspective all that linguistics has accomplished up to now is to map out the functionalities which can serve as input to neuro-linguistics and which it will have to account for at the neuro-physiological level - much like the experimetal laws of physics that serve as the empirical input to abstract physical theories such as statistical mechanics, electromagnetism, quantum mechanics, etc.. Until recently I thought that such a neuro-linguistics would be an enterprise of some far distant future. But it now looks as if we are getting quit close to the point where it is becoming possible to ask substantive questions about how linguistic information is stored and about the neuro-physiological implementation of the processing of linguistic input and output. nd we see the first beginnings of provisonal answers to such questions in the light of what is being learnt about the neural implementation of the storing and processing of information generally.

One of the first (and very preliminary) "results" of explorations in this direction is te relaisation that the basic concepts of linguistics - and especially those of semantics - have to be thought through anew. An example is the notion of predication, i.e. the relation which holds between a predicate and a term when the predicate is (judged to be) true of the object denoted by the term. This is evidently one of the most basic concepts of semantics, and in most current linguistic work it is pretty much taken for granted. But when start to think seriously about how that which manifests itself as a predicational judgement (or as a judgement involving one or more predications) at the level of consciousness of the language user may be implemented at the neurological level, it becomes evident very quickly that many more distinctions have to be drawn than are dreamt of in current semantic theory.

This is no more than one of a few first, small and diffident steps into almost virgin territory. Nevertheless I see it as possible that we will see in the coming years an accelerating development in this direction, quantitatively and qualitatively; and tht this will become one of the principla new directions in which the study of human language will turn.

But, as indicated, there are other developements and reorientations of linguitic theory which we have encountered in the course of this brief resum?. I conclude with a list of these:

1. Natural language semantics increasingly takes on the complextion of a branch of a general theory of information representation and transformation.

2. The role of logical inference in the processes of linguistic interpretation indicates an interleaving of inferential and other representation-manipulating operations. This suggests that the inferential relations and operations that have often been considered the essence of logic are better seen as an integral part of a wider repertoire. Thus logic comes to look much more like a general theory of information, than as a discipline concerned more or less exclusively with deduction

3. Even at that level of linguistic theory where we try to deal just with the judgements of meaning and grammaticality there seems to be a need for semantic representations of different forms. When we descend to the level of mental processes that begins to be discernable in the rsults of psycholinguistics, however, yet other modes of representation seem required. Exactly what these will prove to be like is still quite unclear. The same is true a fortiori for the "logic" of these representations, as well as for the "logic" which connects representations at this level with those mentioned under 2.

4. We are seeing the very first beginnings of a new discipline of "neurosemantics" (Klein, 2000), with its own level of representation and, presumably, its own logic to go with that. And here too, we will have to address the question how representations at this level connect with those "higher up", those postulated by psycho-linguistics and, even higher up, the ones that are currently being used in the kinds of dynamic semantics about which this resum? has been most explicit.

Fragmentary Bibliography

Kamp, H & U Reyle. From Discourse to Logic. Kluwer, 1993.

Klein, M., A neural Theory of Reference, ms, University of Stuttgart, 2001.

Reyle, U. Dealing with Ambiguities by Underspecification: Construction, Representation and Deduction. Journal of Semantics, Vol 5, 1993.

Van Der Sandt, R. Presupposition Projection as Anaphora Resolution, Journal of Semantics, Vol 4, 1992.