## 1 Introduction  
The pervasive integration of artificial intelligence (AI) and machine learning (ML) across diverse sectors has precipitated the unprecedented collection and analysis of personal data, intensifying concerns about privacy and regulatory compliance. Landmark regulations like the European Union's GDPR [1] and California's CCPA [2] enshrine the \"right to be forgotten\", compelling organizations to erase individual data upon request and eliminate its influence from trained models. Traditional machine unlearning in centralized systems addresses this through model retraining after data deletion--a process that becomes prohibitively expensive and impractical in federated learning (FL) environments [3, 4], where data is inherently distributed across edge devices, and central aggregation violates privacy principles. As illustrated in Figure 1, the primary objective of unlearning is to remove specific data points' effects from a trained model while preserving the model's overall performance. Federated learning [5] emerged as a privacy-preserving alternative, enabling collaborative model training by exchanging parameter updates instead of raw data. However, removing a client's data contribution post-training--known as federated unlearning--introduces unique challenges. Decentralized architecture and iterative aggregation of updates make it difficult to isolate and eliminate specific data influences once integrated into the global model [6]. Naive solutions (e.g., retraining from scratch without the target client's data) incur excessive communication and computational overhead [7], while existing unlearning methods (e.g., FedEraser [6]) suffer critical limitations as follows:  
1. Efficiency--storing historical gradients or performing calibration rounds imposes high storage/server costs [8]. 2. Contextual blindness--uniform treatment of data points during unlearning risks unnecessary accuracy loss by disregarding semantic relevance [9]. 3. Verifiability--clients cannot independently confirm complete data erasure [10]. Figure 2 illustrates the working of the typical FL setup. Several clients individually train their ML models, which are then combined into a global model. After this enhancement, the global model is shared with all clients by the server for the training phase in the next FL round. In this way, the international model will continue being processed until it converges. Hence, we want FU to enable the FL model to forget any knowledge about an FL client or any identifiable value linked to a client's partial data, with strict guarantees on the underlying privacy promises of the decentralized learning. To overcome these gaps, we propose two novel federated unlearning frameworks:  
Figure 1: Overview of machine unlearning. Figure 2: Overview of federated unlearning. * EG-FedUnlearn--A gradient-based approach that analytically reverses target clients' contributions from aggregated model parameters. By applying negative gradient updates derived from local data samples, it achieves \"exact unlearning\" (equivalent to retraining) under standard FL assumptions, eliminating retraining costs and minimizing communication. Ontologies are essentially knowledge structures that help in the categorization of knowledge in terms of its entities, attributes, and relations between concepts [10]. With the inclusion of ontology, relevance-based data prioritization can be included in federated unlearning by ensuring the unnecessary data points are forgotten, but those with a larger contextual relevance are kept. Relevance-based ontology provides a way of intelligent unlearning, which is adaptive to context, with the categorization of data and the assignment of relevance scores to the context for each data point to be unlearned. Through this structured relevance-based approach, the model can focus on the high-value information that needs to be retained, thus increasing the efficiency and accuracy of federated unlearning [11]. * OFU-Ontology--The first method to integrate domain ontologies into federated unlearning.