Recently, Large Language Model (LLM)-based Fault Localization (FL) techniques have been proposed, and showed improved performance with explanations on FL results. However, a major issue with LLM-based FL techniques is their heavy reliance on LLMs, which are often unreliable, expensive, and difficult to analyze or improve. When results are unsatisfactory, it is challenging both to determine a cause and to refine a technique for better outcomes. To address this issue, we propose LogicFL, a novel logical fault localization technique for Null Pointer Exceptions (NPEs). With logic programming, LogicFL imitates human developers' deduction process of fault localization, and identifies causes of NPEs after logical inferences on collected facts about faulty code and test execution. In an empirical evaluation of 76 NPE bugs from Apache Commons projects and the Defects4J benchmark, LogicFL accurately identified the fault locations and pinpointed the exact code fragments causing the NPEs for 67 bugs (88.16%), which were 19.64% and 4.69% more bugs than two compared LLM-based FL techniques respectively. In addition, LogicFL can be executed on a low-performance machine similar to a typical laptop, with an average runtime of 21.63 seconds and a worst-case time of under two minutes, including test execution and output file generation. Moreover, when compared to the two LLM-based FL techniques using the GPT-4o model, LogicFL was significantly more cost-efficient, as those techniques required 343.94 and 3,736.19 times the cost of LogicFL, respectively. Last but not least, the deduction process in LogicFL for providing FL results is fully traceable, enabling us to understand the reasoning behind the technique's outcomes and to further enhance the technique.