Transitive inference has been historically touted as a hallmark of human cognition. However, the ability of non-human animals to perform this type of inference is being increasingly investigated. Experimentally, three main methods are commonly used to evaluate transitivity in animals: those that investigate social dominance relationships, the n-term task series and the less well known associative transitivity task. Here, we revisit the question of what exactly constitutes transitive inference based upon a formal and habitual definition and propose two essential criteria for experimentally testing it in animals. We then apply these criteria to evaluate the existing body of work on this fundamental aspect of cognition using exemplars. Our evaluation reveals that some methods rely heavily on salient assumptions that are both questionable and almost impossible to verify in order to make a claim of transitive inference in animals. For example, we found shortcomings with most n-term task designs in that they often do not provide an explicit transitive relationship and/or and ordered set on which transitive inference can be performed. Consequently, they rely on supplementary assumptions to make a claim of transitive inference. However, as these assumptions are either impossible or are extremely difficult to validate in non-human animals, the results obtained using these specific n-term tasks cannot be taken as unambiguous demonstrations (or the lack thereof) of transitive inference. This realisation is one that is generally overlooked in the literature. In contrast, the associative transitivity task and the dominance relationship test both meet the criteria for transitive inference. However, although the dominance relationship test can disambiguate between transitive inference accounts and associative ones, the associative transitivity test cannot. Our evaluation also highlights the limitations and future challenges of current associative models of transitive inference. We propose three new experimental methods that can be applied within any theoretical framework to ensure that the experimental behaviour observed is indeed the result of transitive inference whilst removing the need for supplementary assumptions: the test for the opposite transitive relation, the discrimination test between two separate and previously non-reinforced items, and the control for absolute knowledge.