A type-theoretical approach to Universal Grammar
This addresses the challenge of formalizing linguistic universals for theoretical linguistics, offering a novel alternative to Chomskyan frameworks.
The paper tackles the problem of defining Universal Grammar by proposing a type-theoretical approach using dependent and polymorphic type theory, resulting in a logic that handles grammatical ambiguity, selectional restrictions, and anaphora with a universal set of morphosyntactic types.
The idea of Universal Grammar (UG) as the hypothetical linguistic structure shared by all human languages harkens back at least to the 13th century. The best known modern elaborations of the idea are due to Chomsky. Following a devastating critique from theoretical, typological and field linguistics, these elaborations, the idea of UG itself and the more general idea of language universals stand untenable and are largely abandoned. The proposal tackles the hypothetical contents of UG using dependent and polymorphic type theory in a framework very different from the Chomskyan ones. We introduce a type logic for a precise, universal and parsimonious representation of natural language morphosyntax and compositional semantics. The logic handles grammatical ambiguity (with polymorphic types), selectional restrictions and diverse kinds of anaphora (with dependent types), and features a partly universal set of morphosyntactic types (by the Curry-Howard isomorphism).