Well-Nested Drawings as Models of Syntactic Structure
Manuel Bodirsky, Marco Kuhlmann, and Mathias Möhl. Well-Nested Drawings as Models of Syntactic Structure. In Proceedings of the 10th Conference on Formal Grammar (FG) and Ninth Meeting on Mathematics of Language (MOL), pages 195–203, Edinburgh, UK, 2005.
There are two major approaches to formal accounts of the syntax of natural language, the proof-theoretic and the model-theoretic approach. Both aim at providing frameworks for answering the question whether a given natural language expression is grammatical. Their methodology, however, is rather different: In a proof-theoretic framework, one tries to set up a system of derivation rules (such as the rules in a context-free grammar) so that each well-formed natural language expression stands in correspondence with a derivation in that system. In contrast, in a model-theoretic framework, one attempts to specify a class of models for natural language expressions and a set of constraints on these models such that an expression is well-formed iff it has a model satisfying all the constraints. The main contribution of this paper is the characterisation of a class of structures that provides a new model-based perspective on Tree Adjoining Grammar (Joshi and Schabes (1997)), a well-known proof-theoretic syntactic framework.