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Sept 30 |
James RogersOn Formalizing Syntax Since at least the mid 20th Century,
formalization of a theory of syntax has generally meant providing a
generative grammar or abstract automaton which either generates or
recognizes a set of mathematical structures which properly analyze the
expressions of the language under study. In practice, this approach
is quite difficult and often involves specification of a great deal of
seemingly arbitrary detail. This has led to at least two sorts of
skepticism about the usefulness of formalization:
--- It is too early in the development of the theory to formalize it.
--- The properties of the usual classes of formal languages do not
seem to coincide with the regularities of natural language, hence
formalization may actually mislead the process of theory formation.
But formalization, in general, has well-known benefits. By expressing
the theory in precise mathematical terms one obtains an unambiguous
statement of the claims the theory is making along with, in principle,
the means to explore their consistency and consequences and to
evaluate them against empirical evidence.
In this talk we will discuss a much broader approach to formalization
of syntax in which the set of intended analyses is defined as a set of
mathematical structures using constraints formalized in the language
of mathematical logic, i.e. using Model-Theory. This provides a very
general language for expressing hypothesized constraints which
supports the successive refinement of the theory; as new constraints
are added, the set of licensed structures becomes a successively
better approximation of the intended set of analyses. Hence, the
benefits of formalization are available at all stages of theory
development.
Of particular interest to us is the Model-Theory of finite structures
(Finite Model-Theory). In this realm, the abstract properties of the
definable sets can often be determined by characterizing them in
automata-theoretic terms. The sets of strings that are definable
using Monadic Second-Order Logic, for instance, turn out to be all and
only those that are recognizable by finite state automata; the sets of
trees that are definable in MSO turn out to yield exactly the
Context-Free Languages, etc.
This answers the question of why formal languages should be relevant
to theories of syntax. A theory can be formalized model-theoretically
if the set of structures it licenses can be picked out by very a very
general class of logical constraints. The formal language theory
serves as a tool for determining the abstract properties of the sets
that are definable in this way. Any theory which can be formalized in
this way, then, will exhibit these abstract properties, not as some
sort of a priori assumption but simply as a consequence of its
definability.
We will lay out some of the foundations of this approach and will
survey a range of results characterizing logical languages of varying
expressiveness in terms of formal systems with correspondingly varying
generative capacity.
------ | 4:00PM 2122 Campbell Hall |