The aim of the dissertation is to shed light on the question of what linguistic knowledge available to children language learners is innate, as opposed to being gleaned postnatally from the environment, and to do it by answering a more basic question: what, if it were innate, would assist language learning, and what would not? The method involves implementing a formal model for learning a basic but quite versatile kind of grammar for natural language syntax using methods borrowed from statistical machine learning, along with theoretical methods from theories of syntax and semantics in linguistics. Experiments using existing grammars as benchmarks will be carried out computing measures of performance commonly accepted by computational linguists to assess the accuracy of competing grammars. Initially the testing will be done on small fragments of the grammar of English, but with a view to eventual scaling up so that the system can be trained on large sets of data deriving from actual natural language use in conversational contexts.