Tom Cornell
A Minimalist Grammar
for Deriving the Copy Language
Arbeitspapiere des SFB 340, Bericht Nr. 79 (1996), 20pp.
DVI (142kb);
Postscript (590kb)
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2-up.
Abstract
In these notes we present a minimalist derivational system modeled
largely on Stabler's (1996) formalization of (ideas from)
Chomsky's (1995) Minimalist Program.
Our intention is to show that an
extremely tightly constrained version of this system can nonetheless
include grammars which generate the language ww for w in
{1,2}*. This language is known to be context-sensitive, and is the basis of
the proofs in Huybregts (1984) and Shieber(1985) for the
non-context-freeness of natural language.
We focus here on an artificial language because it is possible to
present a complete grammar which provably generates it. While the
formalism is provably powerful enough to support grammars for
(at least some) mildly
context sensitive languages, it remains computationally attractive. In
particular, its essentially linear use of lexical resources means that
it should be decidable. This in turn may help to suggest ways to
extend decidable grammar logics such as those
presented in Rogers (1994) and Kracht (1995)
beyond their current strictly context-free
power without losing decidability.
Our concern here is mainly to isolate what we hope is the minimal
apparatus necessary to derive strings in Lww in a Chomsky-style
Merge & Move calculus. It turns out we will in fact need very
little. As might be expected from the natural languages which
exemplify Lww-like behavior, we will only need head-movement. So,
a fortiori, we will not need successive cyclic movement. This
means we can stay within the ``linear'' fragment: every movement operation
consumes some resources, and no operation increases resources.
We will also need only one type of feature, namely categorial features
(surely the minimal minimalist feature!) and their checking
counterpart, selectional features. This means we will essentially be
working in a categorial grammar with movement.
Seminar für Sprachwissenschaft
University of Tuebingen
Wilhelmstr. 113
72074 Tübingen
Germany
cornell@sfs.nphil.uni-tuebingen.de