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Applying Logic to the Study of Human Language Syntax

Lecturer: Geoffrey K. Pullum

(University of Edinburgh, UK, and Brown University, USA)

This course provides a brief introduction to some key aspects of grammar in human languages, and considers how to use techniques from mathematical logic to enhance the explicitness of syntactic theories and descriptions. Lecture 1 offers a short overview of the kind of phenomena that syntax deals with, and the kinds of structural representation that linguists use. Lecture 2 surveys the approach to syntactic theory that emerged from formalized proof theory between 1920 and 1940: Generative-Enumerative Syntax (GES). GES gave rise to formal language theory and the classification of sets of strings according to the expressive power of the GES grammars or automata defining them. The remaining three lectures address a less-studied alternative, called Model-Theoretic Syntax (MTS). Lectures 3 and 4 review the interpretation of logical calculi on finite relational structures, outline the central concepts of descriptive complexity theory, and then examine relevant results relating to several different logics on tree-like graph structures of 1 dimension (strings), 2 dimensions (standard trees), and arbitrary dimensions, applying them to the description of human language syntax. In lecture 5, returning to syntactic phenomena, I give some reasons for thinking that MTS frameworks might be better suited to natural language syntax than GES.

Download: main reference paper

Course slides: Lec 1  Lec 2  Lec 3  Lec 4  Lec 5

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