Tom Cornell's Research Interests
My interests lie in or near the intersection of Computational Linguistics, Formal Grammar and Cognitive Science. Trying to be as brief as possible, I suppose I would say that I am interested in Grammar as an example of an interpreted symbol system having both mathematical and natural models. Such a study is naturally intimately tied to the study of formal languages, but considerable care must be taken in getting clear about the role that formal languages play in the study of natural language. In a study such as this ``formal languages'' appear in two places: as the formula languages in which descriptions of natural languages are written down and as the structures which are picked out as the mathematical models of such descriptions. A hard and fast distinction between these cases is hard to draw, since sometimes linguistic formula languages are designed so as to have orthographic sentences among their theorems or productions. Still it is important to keep in mind that the study of formal grammar is not an obsession with the tools of the trade at the expense of the trade itself!
I make this point because I was brought up in a firmly Chomskyan tradition, in which, in recent decades, the study of formal languages has been disparaged. According to the tenets of this tradition a Language, being a thing which a Person can be said to Know, is a Thing Psychological, and so ultimately a phenomenon of the natural world and a fit object of an empirical natural science. A Grammar, from this perspective, is a theory of a language, which isolates certain (mainly structural) properties of the language in question for further study. In such a world view it appears that formal languages are left little place. They are Things Mathematical, and belong to a completely different realm of study, the deductive sciences. However, once we have grammars stated at a reasonable level of precision we find that they have mathematical models as well as their intended natural model. That is, they cannot help but be about certain classes of mathematical structures as well as being about some given natural language. It is these--perhaps unintended--models of the theory that bring formal languages back into the field of avowedly empirical linguistics, and it is their relationship to natural languages on the one hand and to theories of natural languages on the other that are of primary interest to formal linguistics.
The focus on formally specifiable mathematical structures is inevitable in the study of computational linguistics, of course, and as a matter of personal history this is how I became interested in the general topic. There is simply no other way to deal systematically with the problem of getting machines to behave as if they knew (something about) a natural language. It is no less valuable in the study of cognitive science. This is so even though the level of formalization required for ordinary scientific discourse is far less than that required for the specification of mechanical procedures. Of course, for that part of cognitive science which deals in modeling cognition as computation, the distinction between cognitive science and computational linguistics is pretty fine. Mainly, the class of machines interpreting a given formal grammar specification is more restricted, and may be neither sound nor complete in their interpretation of it. More generally, however, if we take the fundamental problem of cognitive science to be the investigation of objects which are notably opaque to direct inspection, then some sort of formal modeling seems inevitable. Accordingly, we reflect such properties of cognition as we are able to observe onto the framework of formal symbolic systems and obtain thereby objects which are transparent to rigorous investigation. (The procedure is the same even if we are pursuing ``sub-symbolic'' approaches to cognition; certainly that approach is no less formal, though the resulting objects are maybe not as transparent as we might like.)
One key problem in the study of any interpreted symbol system, in logic, computer science and grammar, is the problem of relating what we might term Procedural interpretations to what we might term Declarative interpretations. In logic this sort of problem is dealt with in the search for soundness and completeness metatheorems; similar sorts of investigations arise in computer science in the attempt to tie a denotational semantics for a programming language to an operational semantics. I have encountered the same problem in several places in linguistics and cognitive science. For example, a few years ago there was some debate in the study of agrammatic aphasia over the propriety of a representational or a procedural account of the deficit. Some rather elementary modeling work showed at least potentially how those two accounts were interdependent and largely compatible. Though from what I understand subsequent data have not been kind to the particular model I was pushing at the time.
More recently, I have become particularly interested in the relationship between declarative representational approaches to grammar to more procedural derivational approaches. This has been a problem in the field of transformational grammar since the advent of ``trace theory'' in the early seventies, and has become more accute with the recent revival of interest in derivational approaches, apparently at the expense of the more representational approaches that characterized work in that field throughout the eighties and into the nineties. So in modern-day transformational grammar this dichotomous declarative/procedural world-view has become a source of tension and struggle, mainly over whether to use movement transformations or well-formedness conditions on chains to account for extraction phenomena in natural language syntax.
As noted, if we turn our attention to logic, for example, we find in the notion of proof an analogue of grammatical derivation, and in the notion of truth in a structure an analogue of declarative constraint-based grammars. And in logic we have as well, for very many interesting logics, soundness and completeness results which tell us that these notions, or their related notions of consequence, are equivalent. Likewise in computer science, where it is much harder to get the denotational and operational semantics of programming languages to line up, nonetheless when or to the extent that they do line up it is a cause for celebration. So it makes sense to me to pay particular attention to the development and investigation of grammatical systems which have both (transformational) derivational aspects and also principle-based representational aspects which are equivalent, in the sense that some analog of soundness and completeness holds.
Two particular topics of interest to me recently, which fall within this broader research program, have been the following.