The assumption that degrees of grammaticality are relevant to linguistic theory dates back at least to [Chomsky(1964)], and on an informal level, graded data are regularly used to support linguistic analyses. A standard case is the claim that subjacency violations result in only mild deviance, while ECP violations cause strong ungrammaticality. The influential study of psych-verbs by [Belletti and Rizzi(1988)] builds on this assumption, making use of no less than seven levels of acceptability.
However, Belletti and Rizzi's treatment of graded data is very casual and provides ``no general theory of which principles should cause worse violations. The theory makes no prediction about the relative badness of, say, -Criterion versus Case Filter violations, let alone about how bad each one is in some absolute sense. The notion of relative and absolute badness of particular violations is ad hoc, and is used in just those cases where it is convenient'' ([Schütze(1996)], p. 43).
This seems to be a typical case: even though the existence of graded linguistic data and its potential significance are generally acknowledged, hardly any effort has gone into the theoretical investigation of graded grammaticality, and none of the established grammatical frameworks offers a systematic account of graded data. To overcome this problem, we propose an extension of Optimality Theory that provides a theoretically sound model of graded grammaticality and makes clear empirical predictions. As a test case, we present an account of gradedness in extraction from picture NPs, based on experimental data from a psycholinguistic study.