Machine learning models are increasingly used in critical areas such as loan approvals and hiring, yet they often function as black boxes, obscuring their decision-making processes. Transparency is crucial, as individuals need explanations to understand decisions, primarily if the decisions result in an undesired outcome. Our work introduces CoGS (Counterfactual Generation with s(CASP)), a model-agnostic framework capable of generating counterfactual explanations for classification models. CoGS leverages the goal-directed Answer Set Programming system s(CASP) to compute realistic and causally consistent modifications to feature values, accounting for causal dependencies between them. By using rule-based machine learning algorithms (RBML), notably the FOLD-SE algorithm, CoGS extracts the underlying logic of a statistical model to generate counterfactual solutions. By tracing a step-by-step path from an undesired outcome to a desired one, CoGS offers interpretable and actionable explanations of the changes required to achieve the desired outcome. We present details of the CoGS framework along with its evaluation.