A property of human language associates words or labels each other according to several arbitrary rules. However, we do not know what cognitive abilities produce this property in humans. Through hierarchical concept acquisition, in this study we investigated the cause of this property in non-human animals, Capuchin monkeys ( Cebus apella ). First, we trained the subjects to acquire four component concepts with symbolic matching-to-sample (SMTS) procedures. Next, we trained the subjects to acquire two higher-order concepts including four acquired component concepts. The monkeys had to learn the relations between the examples of four component and two higher-order concepts and geometrical figures used as symbols in the SMTS tasks. Thereafter, we tested whether the monkeys spontaneously acquire relations among symbols similar with the hierarchy among concepts without particular training. Test results indicated that the monkeys understood that the symbols associated with component concepts were in relation to the symbols associated with higher-order concepts; on the other hand, they showed no evidence of understanding the opposite relations. It suggests that they could find an association among symbols based on hierarchy among concepts; however, their ability to grasp associations among symbols based on arbitrary rules was limited compared to humans.