To successfully learn language—and more specifically how to use verbs correctly—children must solve the linking problem: they must learn the mapping between the thematic roles specified by a verb’s lexical semantics and the syntactic argument positions specified by a verb’s syntactic frame. We use an empirically grounded and integrated quantitative framework involving corpus analysis, experimental meta-analysis, and computational modeling to implement minimally distinct versions of mapping approaches that (i) either are specified a priori or develop during language acquisition, and (ii) rely on either an absolute or a relative thematic role system. Using successful verb class learning as an evaluation metric, we embed each approach within a concrete model of the acquisition process and see which learning assumptions are able to match children’s verb-learning behavior at three, four, and five years old. Our current results support a trajectory where children (i) may not have prior expectations about linking patterns between ages three and five, and (ii) begin with a relative thematic system, progressing toward optionality between a relative and an absolute system. We discuss implications of our results for both theories of syntactic representation and theories of how those representations are acquired. We also discuss the broader contribution of this study as a concrete modeling framework that can be updated with new linking theories, corpora, and experimental results.