In recent years, research efforts have been directed towards the use of Machine Learning (ML) techniques to support and automate activities such as specification mining, risk assessment, program analysis, and program repair. The focus has largely been on the use of machine learning black box methods whose inference mechanisms are not easily interpretable and whose outputs are not declarative and guaranteed to be correct. Hence, they cannot readily be used to inform the elaboration and revision of declarative software models identified to be incorrect or incomplete. On the other hand, recent advances in ML have witnessed the emergence of new logic-based machine learning approaches that overcome such limitations and which have been proven to be well-suited for many software engineering tasks. In this chapter, we present a survey of the state-of-the-art of logic-based machine learning techniques, highlight their expressivity, define their different underlying semantics, and discuss their efficiency and the heuristics they adopt to guide the search for solutions. We then demonstrate the application of this type of machine learning to (declarative) specification refinement and revision as a complementary task to program analysis.