Discontinuity And The Lambek Calculus

This paper is concerned with tile treatment of discontinuous constituency within Categorial Grammar. In particular, I address the problem of providing an adequate formalisation of categorial commctives l)rol)osed by Moortgat (1988), which are useful for handling certain forms of diseontimmus eonstitnency, l)espite some interesting proposals, a satisfactory logic for these e{mnectives has so far remained dnsive. I will provide such a h)gie, using an approach that falls within the general framework of labelled deductive systems (Gabbay, 1991), employing novel methods for reasoning ahout linear order in resource nsage. The approach is illusl;rated by linguistic al}plications for extraction, pied-piping and quanti[ieation.