  We introduce (1) a novel parser for Minimalist Grammars (MG), encoded as a
system of first-order logic formulae that may be evaluated using an SMT-solver,
and (2) a novel procedure for inferring Minimalist Grammars using this parser.
The input to this procedure is a sequence of sentences that have been annotated
with syntactic relations such as semantic role labels (connecting arguments to
predicates) and subject-verb agreement. The output of this procedure is a set
of minimalist grammars, each of which is able to parse the sentences in the
input sequence such that the parse for a sentence has the same syntactic
relations as those specified in the annotation for that sentence. We applied
this procedure to a set of sentences annotated with syntactic relations and
evaluated the inferred grammars using cost functions inspired by the Minimum
Description Length principle and the Subset principle. Inferred grammars that
were optimal with respect to certain combinations of these cost functions were
found to align with contemporary theories of syntax.
