Generative linguists think that for native speakers of natural languages, grammaticality is a matter of linguistic intuition, a competence learned by language acquisition in childhood and therefore strive to predict grammaticality exhaustively. On the other hand, there is a gradual abandonment of grammaticality in favour of acceptability by linguists that stress the social acquisition of language in contrast to innate factors (and who will seldom rely on phrase structure grammar) in the tradition of Hopper 1987. Prescriptive grammars of controlled natural languages define grammaticality as a matter of explicit consensus.
Hopper, Paul (1987): Emergent grammar. In: Aske, Jon et al. (ed.) (1987): General session and parasession on grammar and cognition. Proceedings of the thirteenth annual meeting. Berkeley: BLS: 139-155.
Lyons, John (1968): Introduction to Theoretical Linguistics. London: Cambridge University Press.
Productivity, Fluency, and Grammaticality Measures from Narratives: Potential Indicators of Language Proficiency?
Sep 22, 2007; The purpose of this study was to identify potential general outcome indicators (GOIs) of language proficiency. Brief narratives...