Abstract Discovering association rules from transaction databases is one of the most studied data mining task. Many effective techniques have been proposed over the years. All these algorithms share the same two steps methodology: frequent itemsets enumeration followed by effective association rules generation step. In this paper, we propose a new propositional satisfiability based approach to mine association rules in a single step. The task is modeled as a Boolean formula whose models correspond to the rules to be mined. To highlight the flexibility of our proposed framework, we also address two other variants, namely the closed and indirect association rules mining tasks. Experiments on many datasets show that on both closed and indirect association rules mining tasks, our declarative approach achieves better performance than the state-of-the-art specialized techniques.