During language acquisition, children are tasked with the challenge of determining which words can appear in which syntactic constructions. This has been long recognized as a learnability paradox. On one hand, there are generalizations that children must learn. On the other hand, language is known for its arbitrariness, so children also need to decide when not to generalize and just resort to memorization. Finally, the picture is further complicated by the lack of negative evidence during language acquisition. In this dissertation, by applying a generalization learning model, The Tolerance/Sufficiency Principle, I provide novel approaches to the acquisition of a range of syntactic generalizations. Chapter 2 examines the acquisition of verb argument structure, where there are systematic syntax-semantics mappings. I argue that knowledge of such syntax-semantics mappings should not and need not be innate. Instead, I propose a computational model that can learn these mappings distributionally from modest-sized input data. I also conduct model comparisons to illustrate that the proposed model yields learning outcomes that are more accurate than a model which relies on Bayesian inference. Chapter 3 moves on to a case where the relation between syntax and semantics is far less systematic - the acquisition of recursive structures. The rules for recursion differ across languages and structures. Through corpus analyses of different recursive structures across languages, I demonstrate that the rules for recursive embedding can be established through purely formal analyses of one-level embedding data, and the core semantic properties such as alienable possession vs. inalienable possession can be identified subsequently. In Chapter 4, I conduct a series of artificial language learning experiments, which find that both adults and children can indeed use purely distributional cues to acquire recursive structures as predicted: They will allow recursive embedding in an artificial grammar when there are sufficient cues in the exposure supporting the generalization, even though they never hear recursively embedded sentences in the exposure phase. Ultimately, this dissertation aims to contribute quantitatively rigorous and psychologically real solutions to a well-known learning problem, offering new perspectives for the mechanisms of learning generalizations.