Logical rule-based methods offer an interpretable approach to knowledge graph completion (KGC) by capturing compositional relationships in the form of human-readable inference rules. While existing logical rule-based methods learn rule confidence scores, they typically assign a global weight to each rule schema, applied uniformly across the graph. This is a significant limitation, as a rule's importance often varies depending on the specific query instance. To address this, we introduce SLogic (Subgraph-Informed Logical Rule learning), a novel framework that assigns query-dependent scores to logical rules. The core of SLogic is a context-aware scoring function. This function determines the importance of a rule by analyzing the subgraph locally defined by the query's head entity, thereby enabling a differentiated weighting of rules specific to their local query contexts. Extensive experiments on benchmark datasets show that SLogic outperforms existing rule-based methods and achieves competitive performance against state-of-the-art baselines. It also generates query-dependent, human-readable logical rules that serve as explicit explanations for its inferences.