Indoor localization using deep learning (DL) has demonstrated strong accuracy in mapping Wi-Fi RSS fingerprints to physical locations; however, most existing DL frameworks function as black-box models, offering limited insight into how predictions are made or how models respond to real-world noise over time. This lack of interpretability hampers our ability to understand the impact of temporal variations - caused by environmental dynamics - and to adapt models for long-term reliability. To address this, we introduce LogNet, a novel logic gate-based framework designed to interpret and enhance DL-based indoor localization. LogNet enables transparent reasoning by identifying which access points (APs) are most influential for each reference point (RP) and reveals how environmental noise disrupts DL-driven localization decisions. This interpretability allows us to trace and diagnose model failures and adapt DL systems for more stable long-term deployments. Evaluations across multiple real-world building floorplans and over two years of temporal variation show that LogNet not only interprets the internal behavior of DL models but also improves performance-achieving up to 1.1x to 2.8x lower localization error, 3.4x to 43.3x smaller model size, and 1.5x to 3.6x lower latency compared to prior DL-based models.