arXiv2026
Modern explainable AI still struggles with a fundamental gap: although Bayesian networks (BNs) provide transparent probabilistic structure, there is no unified way to formally express, query, and verify what these models imply. Analysts often rely on ad hoc queries, manual interventions, or informal reasoning to explore causal relations and hypothetical scenarios, making it difficult to systematically validate model behaviour, uncover hidden assumptions, and guarantee reliability. We introduce BayesL (pronounced Basil), a logical framework for specifying, querying, and verifying the behaviour of BNs. BayesL is a structured language that supports both probabilistic inference queries (e.g., marginal, conditional, MAP) and model-checking-style queries that specify formal properties of BN behaviour. It facilitates versatile reasoning over causal and evidential relationships, including counterfactual what-if scenarios via conditional probability tables updates, without requiring manual modifications to the model. In addition to graph structure reasoning and inference, BayesL enables the formal specification of properties, supported by dedicated model checking algorithms and a preliminary open-source implementation. By allowing inference and verification within a single formal language, BayesL establishes a white-box verification paradigm in which model structure, assumptions, and reasoning processes are explicitly encoded and systematically checked. We demonstrate this through two diagnostic case studies and a benchmark set of BN models, showing how BayesL clarifies BN behaviour in a precise and analyzable way, advancing the transparency, trustworthiness, and practical explainability of BN-based systems.