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:
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.