Although the observation of grammaticality judgements is well acknowledged, their formal representation faces problems of different kinds: linguistic, psycholinguistic, logical, computational. In this paper we focus on addressing some of the logical and computational aspects, relegating the linguistic and psycholinguistic ones in the parameter space. We introduce a model-theoretic interpretation of Property Grammars, which lets us formulate numerical accounts of grammaticality judgements. Such a representation allows for both clear-cut binary judgements, and graded judgements. We discriminate between problems of Intersective Gradience (i.e., concerned with choosing the syntactic category of a model among a set of candidates) and problems of Subsective Gradience (i.e., concerned with estimating the degree of grammatical acceptability of a model). Intersective Gradience is addressed as an optimisation problem, while Subsective Gradience is addressed as an approximation problem. © 2011 Springer-Verlag.
Duchier, D., Prost, J. P., & Dao, T. B. H. (2011). A model-theoretic framework for grammaticality judgements. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5591 LNAI, pp. 17–30). https://doi.org/10.1007/978-3-642-20169-1_2