Transitive inference has traditionally been regarded as a relational proposition-based reasoning task, however, recent investigations question the validity of this assumption. Although some results support the use of a relational proposition-based approach, other studies find evidence for the use of associative learning. We examined whether participants are biased towards a relational proposition-based approach, or associative learning, depending upon the integrity of other cognitive abilities supported by frontal and medial temporal lobes. We found that transitive inference success and strategy use are related to tasks that require processing of, and memory for, relations. Participants who showed superior memory for relations among items showed superior transitive inference accuracy, and conversely, participants who showed superior memory for single items showed inferior transitive inference accuracy. Participants who demonstrated performance patterns indicative of a proposition-based approach showed more accurate inference performance, and superior memory for, and online access to, relations among items. Participants who demonstrated performance patterns indicative of associative learning showed inferior transitive inference accuracy and superior iconic/pictorial abilities. We speculate that transitive inference performance is mediated by interactions among multiple cognitive systems that support different aspects of processing, from which the degree of contribution varies depending on underlying cognitive/neural integrity.