Human reasoning relies on abstraction and generalization, in order to make decisions flexible under changing conditions while ignoring irrelevant details and focusing on the essence. Developing AI systems with such abilities, while ensuring transparency and explainability on the reasoning behind the made decision, remains a central challenge. Symbolic AI provides transparent knowledge representations and formal reasoning guarantees, yet lacks principled mechanisms for abstracting away irrelevant details while preserving the information required for reasoning, explainability, and generalization. This paper presents an overview of my research towards addressing this challenge by developing formal and computational methods for abstraction in Answer Set Programming, one of the core formalisms in symbolic AI, and related logic-based frameworks. The contributions span from foundational abstraction techniques that simplify reasoning representations while preserving essential solution properties, to investigations on how such abstractions can both improve computational reasoning and support human understanding of AI decision processes.