Parsing as Deduction Revisited: Using an Automatic Theorem Prover to Solve an SMT Model of a Minimalist Parser

Abstract

We introduce a constraint-based parser for Minimalist Grammars (MG), implemented as a working computer program, that falls within the long established “Parsing as Deduction” framework. The parser takes as input an MG lexicon and a (partially specified) pairing of sound with meaning - i.e. a word sequence paired with a semantic representation - and, using an axiomatized logic, declaratively deduces syntactic derivations (i.e. parse trees) that comport with the specified interface conditions. The parser is built on the first axiomatization of MGs to use Satisfiability Modulo Theories (SMT), encoding in a constraint-based way the principles of minimalist syntax. The parser operates via a novel solution method: it assembles an SMT model of an MG derivation, translates the inputs into SMT formulae that constrain the model, and then solves the model using the Z3 SMT-solver, a high-performance automatic theorem prover; as the SMT-model has finite size (being bounded by the inputs), it is decidable and thus solvable in finite time. The output derivation is then recovered from the model solution. To demonstrate this, we run the parser on several representative inputs and examine how the output derivations differ when the inputs are partially vs. fully specified. We conclude by discussing the parser’s extensibility and how a linguist can use it to automatically identify: (i) dependencies between input interface conditions and principles of syntax, and (ii) contradictions or redundancies between the model axioms encoding principles of syntax.