Before a linguistic model for graded grammaticality can be proposed, the empirical properties of graded data have to be clarified. In psycholinguistics, there exists a considerable amount of research on graded acceptability judgments (cf. [Schütze(1996)] for an overview) and recently, [Bard et al.(1996)Bard, Robertson, and Sorace] have proposed magnitude estimation as a method for obtaining reliable and fine-grained linguistic judgments. This experimental method has been successfully applied to phenomena such as auxiliary selection (cf. [Sorace(1993a)]), unaccusativity (cf. [Sorace(1993b)]), and extraction (cf. [Keller(1996)]).
Our proposal relies on the experimental results of [Keller(1996)], which show that the following factors have a significant influence on the acceptability of extraction from picture NPs: definiteness of the picture NP (indefinite vs. definite determiner), aspectual class of the matrix verb, referential specificity of the extracted NP (which N, how many N, who, what). Keller's experimental data consists of numerical acceptability rating, normalized and averaged over 19 subjects. The data includes the following acceptability hierarchy for the parameters definiteness of the picture NP and referential specificity of the extracted NP (which N, how many N).
Figure 1: Experimentally found acceptability ratings