Abstract
The question of the logical modelling of natural language is concerned with providing a formal framework, which enables representing and reasoning about utterances in natural language. The body of work in this area is organised around two different hypotheses, which yield significantly different notions of what the object of study is. Each of those two hypotheses is based on a different side of Logic: the proof-theoretic hypothesis, and the model-theoretic one. The proof-theoretic hypothesis, on one hand, considers that natural language can be modelled as a formal language. It sets the syntax of the observed natural language at the syntax level of the modelling formal language. All the works based on Generative Grammar rely on this hypothesis. The model-theoretic hypothesis, on the other hand, considers that natural language, along all its dimensions including Syntax, must be modelled through the semantic level of Logic. Underlying are two fairly different notions of what natural language is — and is not, and what should — or not — be modelled.We introduce and compare the main characteristics of both the Proof-Theoretic and the Model-Theoretic paradigms. We argue that representing the linguistic description of an utterance solely through a hierarchical syntactic structure is severely restrictive. We show evidence of these restric- tions through the study of specific problems. We then argue that a Model- Theoretic representation of Syntax does not show those restrictions, and provides a more informative linguistic description than Proof-Theoretic Syntax. We give an overview of a specific framework for MTS, called Property Grammar (PG), which we use to illustrate our point. We show, in particular, how to rely on a graph as linguistic representation, in order to address various language problems.