Formal Foundations of Model-Theoretic Syntax

James Rogers

Description:

  The central idea of Model-Theoretic Syntax is to define sets of syntactic
structures as ordinary relational structures using standard logical languages.
Grammars, in essence, are sets of axioms defining the class of structures
licensed by some particular theory of syntax.  This approach is natural for
principle- or constraint-based theories.  More surprisingly, it works equally
well for many theories stated in terms of generative mechanisms.  Thus MTS
provides a uniform framework for formalizing theories stated in widely
disparate terms, one in which all assumptions about the relevant properties of
the underlying models are made explicit.  Moreover, effective characterizations
in automata-theoretic terms have been developed for the classes of structures
definable in a variety of logical languages, providing a foundation for
algorithms for processing languages defined using these descriptive mechanisms.

  Although its roots can be traced to Arc-Pair Grammar of the early 80's (and
to the formal semantics of formalisms such as GPSG, LFG, and HPSG) most of the
active development of the field has occurred over the last ten years, with
considerable growth in interest over the last couple of years including a
session on MTS within the FG/MOL conference at ESSLLI'01 and a week long
workshop at NASSLLI'02.  This course will focus on the logical and
automata-theoretic foundations of the approach as well as on formal issues in
interpreting existing theories of syntax.  Examples will be drawn from GB,
GPSG, LFG, Minimalist grammars and others and will survey recent work by
Blackburn, Cornell, Kracht, Langholm, Morawietz, Rogers and others.

  We will assume only basic familiarity with First-Order Logic and Formal
Language Theory.  Some familiarity with the grammar formalisms in question
would make the examples more immediately accessible, but will not be
essential. 

  This is a revision and extension of a similarly titled course given at
ESSLLI'03.