A type-theoretical approach to Universal Grammar

TL;DR

This paper proposes a novel type-theoretical framework for representing natural language structure, aiming to address limitations of traditional Universal Grammar theories through a precise, universal, and flexible logical system.

Contribution

It introduces a dependent and polymorphic type logic for natural language, offering a new formal approach distinct from Chomskyan theories of Universal Grammar.

Findings

Handles grammatical ambiguity with polymorphic types

Models diverse anaphora using dependent types

Provides a partly universal set of morphosyntactic types

Abstract

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).