Association rule mining is one of the well-studied and most important knowledge discovery task in data mining. In this paper, we first introduce the k-disjunctive support based itemset, a generalization of the traditional model of itemset by allowing the absence of up to k items in each transaction matching the itemset. Then, to discover more expressive rules from data, we define the concept of (k, k′)-disjunctive support based association rules by considering the antecedent and the consequent of the rule as k-disjunctive and k′-disjunctive support based itemsets, respectively. Second, we provide a polynomial-time reduction of both the problems of mining k-disjunctive support based itemsets and (k, k′)-disjunctive support based association rules to the propositional satisfiability model enumeration task. Finally, we show through an extensive campaign of experiments on several popular real-life datasets the efficiency of our proposed approach