We introduce LK,P2β, a monadic second-order language for reasoning about
trees which characterizes the strongly Context-Free Languages in the sense that
a set of finite trees is definable in LK,P2β iff it is (modulo a
projection) a Local Set---the set of derivation trees generated by a CFG. This
provides a flexible approach to establishing language-theoretic complexity
results for formalisms that are based on systems of well-formedness constraints
on trees. We demonstrate this technique by sketching two such results for
Government and Binding Theory. First, we show that {\em free-indexation\/}, the
mechanism assumed to mediate a variety of agreement and binding relationships
in GB, is not definable in LK,P2β and therefore not enforcible by CFGs.
Second, we show how, in spite of this limitation, a reasonably complete GB
account of English can be defined in LK,P2β. Consequently, the language
licensed by that account is strongly context-free. We illustrate some of the
issues involved in establishing this result by looking at the definition, in
LK,P2β, of chains. The limitations of this definition provide some insight
into the types of natural linguistic principles that correspond to higher
levels of language complexity. We close with some speculation on the possible
significance of these results for generative linguistics.Comment: To appear in Specifying Syntactic Structures, papers from the Logic,
Structures, and Syntax workshop, Amsterdam, Sept. 1994. LaTeX source with
nine included postscript figure