A Bayesian network is a probabilistic graphical model. Many conventional methods have been proposed for its construction. However, these methods often result in an incorrect Bayesian network structure. In this study, to correctly construct a Bayesian network, we extend the concept of propositional logic. We propose a methodology for constructing a Bayesian network with causal relationships that are extracted only if the antecedent states are true. In order to determine the logic to be used in constructing the Bayesian network, we propose the use of association rule mining such as the Apriori algorithm. We evaluate the proposed method by comparing its result with that of traditional method, such as Bayesian Dirichlet equivalent uniform (BDeu) score evaluation with a hill climbing algorithm, that shows that our method generates a network with more necessary arcs than that generated by the traditional method.