Extended Abstract

Incremental Acquisition of a Minimalist Grammar using an SMT-Solver

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Abstract

We introduce a novel procedure that uses the Z3 SMT-solver, an interactive theorem prover, to incrementally infer a Minimalist Grammar (MG) from an input sequence of paired interface conditions, which corresponds to the primary linguistic data (PLD) a child is exposed to. The procedure outputs an MG lexicon, consisting of a set of (word, feature-sequence) pairings, that yields, for each entry in the PLD, a derivation that satisfies the listed interface conditions; the output MG lexicon corresponds to the Knowledge of Language that the child acquires from processing the PLD. We use the acquisition procedure to infer an MG lexicon from a PLD consisting of 39 simple sentences with at most one level of embedding. Notably, the inferred lexicon can generate a countably infinite set of derivations, including derivations with n-levels of embedding for any n>0, thereby generalizing beyond the input PLD. The acquisition procedure allows us to focus on specifying the learner’s initial state and conditions on the learner’s final state (imposed by the PLD), and leave to the solver questions of how the language-acquisition device goes from the initial state to the final state and what that final state is.

Keywords: Minimalist Grammar, MG, Inference, SMT, Satisfiability Modulo Theories, SMT solver, Z3, Minimalist Program, Syntax, Minimalist Syntax, Language Acquisition, Modeling, Interface Conditions, Lexicon, Derivation

How to Cite:

Indurkhya, S., (2022) “Incremental Acquisition of a Minimalist Grammar using an SMT-Solver”, Society for Computation in Linguistics 5(1), 212-216. doi: https://doi.org/10.7275/0eh9-5w03