Creating a descriptive grammar of a language is an indispensable step for language documentation and preservation. However, at the same time it is a tedious, time-consuming task. In this paper, we take steps towards automating this process by devising an automated framework for extracting a first-pass grammatical specification from raw text in a concise, human- and machine-readable format. We focus on extracting rules describing agreement, a morphosyntactic phenomenon at the core of the grammars of many of the world’s languages. We apply our framework to all languages included in the Universal Dependencies project, with promising results. Using cross-lingual transfer, even with no expert annotations in the language of interest, our framework extracts a grammatical specification which is nearly equivalent to those created with large amounts of gold-standard annotated data. We confirm this finding with human expert evaluations of the rules that our framework produces, which have an average accuracy of 78%. We release an interface demonstrating the extracted rules.