As a test case for our model of graded grammaticality, we propose an account of gradedness in extraction from picture NPs, capturing the experimental data of [Keller(1996)]. Our account builds on the OT analysis of extraction proposed by [Legendre et al.(1995)Legendre, Wilson, Smolensky, Homer, and Raymond], using the following of their constraints:
: a chain link must not cross n
barriers
: a
non-referential chain link must not cross n barriers
To capture the definiteness effect in extraction, we incorporate insights
from account of indefinite NPs proposed by [Diesing(1992)]. Her
Mapping Hypothesis is implemented in OT via the domain operators Res
and Ex, which form chains 
and 
and are subject to the constraint *Op
(instantiated as *Ex, *Res). To account for the referentiality effect,
we assume that wh-chains 
can be classified as referential (as with
which man) or non-referential (as with how many men),
and hence are subject to Legendre et al.'s constraints
(1) and (2).
Figure 2: Candidate set for proposed ranking
Figure 3: Candidate set for alternative ranking
We assume the constraint ranking 
, which is a
straightforward extension of the one proposed by
[Legendre et al.(1995)Legendre, Wilson, Smolensky, Homer, and
Raymond]. This ranking yields the candidate set in
fig. 2 for the data in fig. 1. Note
that the harmony ranking (and hence the grammaticality ranking) reflects
precisely the acceptability ranking found in the experimental data.
This example demonstrates how graded OT allows to determine constraint
rankings on the basis of evidence from suboptimal candidates. In
graded OT, a given ranking predicts not only the optimal structure for
for a candidate set (as in standard OT), but also a grammaticality hierarchy
for the suboptimal structures. A single change in the ranking can
alter the order of the suboptimal candidates dramatically, hence the
correct prediction of a complete grammaticality hierarchy constitutes strong
evidence for a given ranking. As an example consider the hierarchy in
fig. 3, which emerges from the alternative ranking
and is competely
different from the empirically found one in fig. 1.
Thus, graded OT can be claimed to enhance the predictive power of
standard OT.