Type Dependency, Type Theory with Records, and Natural-Language Flexibility

There has recently been a surge of interest in the use of rich type systems (with, variously, record types, subtyping, and/or dependent intersections) in order to express various linguistic phenomena at various levels : subsententially there are applications to lexical semantics, sententially one sees accounts of syntax, and in the realm of which is traditionally called pragmatics one finds accounts of dialogue that are markedly more subtle than the usual pragmatic treatment. Something is surely being done right.

Questions, however, remain. Scope, and other syntactic issues, still seem to be quite tricky, and the complexity of the type systems that are being used makes it difficult to say whether the difficulties are problems in principle or merely problems of implementation. The question of the semantics of these systems — that is, semantics in the everyday sense, rather than semantics in the sense of model theory — remains largely unexamined, and the field remains quite open : it is not clear whether we need a semantics in the traditional sense (possibly enriched with vector spaces or the like), or whether proof theory might not be a more suitable way of connecting these formalisms to the observed phenomena of linguistics. Proof theory seems, prima facie, to be more philosophically appealing, but at the cost of greater technical difficulty. Finally, there is the question of how these approaches are connected with more algebraic approaches to syntax, which also have their appeal.

All of these considerations, furthermore, are quite high level, and do not lead directly to concrete models of language or language processing. Girard’s theory of ludics has also enjoyed considerable interest, not least because it is a theory which seems to be descriptively very capable but whose foundations are very simple and very low-level. It could, then, either illuminate or short-circuit many of the above quarrels.

This workshop will explore these problems in some depth, endeavouring to respect both the technical issues and the empirical reality of linguistics : we have assembled a group of speakers of a variety of backgrounds but all of them with something to say to each other.