Solving for syntax

Abstract

Among the key questions that have guided research into the nature of human language for the past sixty years, two have been particularly salient: (1) What constitutes knowledge of language? and (2) How is that knowledge acquired? In particular, children using limited input examples, in effect small "sample size" complexity, all acquire their native language. This thesis attempts to answer these two questions by developing a novel, explicit, computational implementation of one contemporary approach to human language known as the Minimalist Program. It provides an answer to question (1) via the explicit axiomatization of a declaratively specified logical model of minimalist grammars, consisting of a set of formally specified principles and a single structure-building operation, along with a lexicon.

By rendering these axioms along with the lexicon as a set of constraints that are expressed using Satisfiability Modulo Theories (SMT), that must be simultaneously satisfied, the thesis demonstrates how to "solve for syntax": it uses an SMT-solver to computationally deduce the syntactic derivations that associate particular input sentences with their logical forms. In this sense, the thesis demonstrates that the proposed linguistic principles underlying such a system, including the contemporary notion of "economy conditions" in syntax are both coherent and consistent, and, importantly, that minimalist syntax can be placed within a classical "parsing as deduction" framework. This thesis then extends the system developed to address question (1) to provide an answer to question (2), by modeling acquisition as the construction of a succession of lexicons, starting from some initial, essentially empty lexicon, and then augmenting that lexicon.

To do this, it uses a set of (input sentence, skeletal "meaning") pairs intended to reflect minimally cognitively faithful constraints to infer what lexicon would bridge from input to quasi-meaning forms, again using an SMT-solver. Using this approach, the thesis explicitly demonstrates that a wide variety of syntactic sentence constructions in English can be acquired in this way, sufficient to account for the infinite generative capacity of at least one portion of English syntax. Importantly then, the thesis thus demonstrates that a contemporary minimalist syntactic system, with a single, fixed structure-building operation leaving only the lexicon to vary, can serve as the foundation for a contemporary approach to language acquisition. In this sense, the implementation serves as a concrete, computationally realized contemporary instantiation of the model of language acquisition set out in Aspects of the Theory of Syntax.