Formal Tools for Describing and Processing Discontinuous Constituency Structure

This contribution is concerned with the development of formal tools for the description and processing of discontinuous constituency structures. It is argued rst that the traditional tree representations of constituent structure are too limited, and that these representations in general should be allowed to have crossing branches. A precise mathematical deenition of discontinuous trees is provided, plus a linear precedence relation for expressing a kind of concatenation operation on these structures. The formal concepts introduced here are theory-neutral and can be applied in a wide variety of grammatical frameworks and their computer implementations. Their use in phrase-structure grammars is explained in some detail, developing a grammatical formalism called Discontinuous Phrase Structure Grammar (DPSG); their possible use in Categorial Grammar is considered very brieey. The paper concludes with a section on computational issues, in particular in relation to the computer implementation of DPSG for parsing and generation.