Copyright 2005 Psychonomic Society, Inc. 742Memory & Cognition2005, 33 (4), 742-750When told that John is taller than Bill, who is tallerthan Fred, one would logically infer that John is tallerthan Fred. This outcome is often referred to as transitiveinference (TI). It is obvious from the above example thatpeople have the capacity to explicitly encode these state-ments (“premises”), make the logical inference, and de-clare the basis of their conclusion. However, this same TIbehavior has been demonstrated in a wide variety of an-imal species (rats, pigeons, and primates; Davis, 1992;Dusek & Eichenbaum, 1997; Van Elzakker, O’Reilly, &Rudy, 2003; von Fersen, Wynne, Delius, & Staddon,1991; Wynne, 1995). Some researchers have assumedthat such animals use a process much like human logicalreasoning to achieve these behavioral results (e.g., Davis,1992; Dusek & Eichenbaum, 1997). Others have arguedthat these behaviors are better understood as resulting fromsubtle differences in the associative strength of the stim-ulus cues (Frank, Rudy, & O’Reilly, 2003; Van Elzakkeret al., 2003; von Fersen et al., 1991; Wynne, 1995). Inthis article, we turn the anthropomorphic bias of the for-mer interpretation on its ear and demonstrate that peoplecan use a nonexplicit means of exhibiting TI-like behav-ior that has distinguishing characteristics of the associa-tive strength mechanisms. Thus, we conclude that peoplecan be added to the list of species that demonstrate TI-likebehavior without relying on explicit logical reasoning.In animals, TI is evaluated by first training a series ofsimultaneous discrimination problems (e.g., A⫹B⫺ ,B⫹C⫺, C⫹D⫺, D⫹E⫺), where “⫹” and “⫺” refer tothe rewarded and nonrewarded choices, respectively.After reaching criterion performance on all training pairs,the animal is tested for inference with novel pairs (e.g.,BD and AE). The successful choice of stimulus B over Dis taken as evidence of TI. Whereas AE performance istrivial—A is always rewarded and E is never rewarded—the same cannot be said about BD, because B and D areequally often rewarded during training. Some then inter-pret successful BD performance to indicate that the ani-mal uses relational information to infer that B is logicallysuperior to D (Dusek & Eichenbaum, 1997). However,more recent findings pose a challenge to this account.Specifically, when another premise pair (E⫹F⫺) is addedto the training paradigm, transitive behavior breaks downin rats (Van Elzakker et al., 2003). When tested, rats re-liably chose B over E, but BD performance did not differstatistically from chance.Whereas a logical inference account predicts similargood performance in both cases, computational model-We thank Terri Zacharias for testing participants at the University of Vir-ginia. This research was supported by ONR Grants N00014-00-1-0246 andN00014-03-1-0428 and National Institutes of Health Grant MH61316.Correspondence concerning this article should be addressed to R. C.O’Reilly or M. J. Frank, Department of Psychology, University of Col-orado, 345 UCB, Boulder, CO 80309 (e-mail: [email protected] [email protected]).When logic fails: Implicit transitive inference in humansMICHAEL J. FRANK and JERRY W. RUDYUniversity of Colorado, Boulder, ColoradoWILLIAM B. LEVYUniversity of Virginia, Charlottesville, VirginiaandRANDALL C. O’REILLYUniversity of Colorado, Boulder, ColoradoTransitive inference (TI) in animals (e.g., choosing A over C on the basis of knowing that A is betterthan B and B is better than C) has been interpreted by some as reflecting a declarative logical inferenceprocess. We invert this anthropomorphic interpretation by providing evidence that humans can exhibitTI-like behavior on the basis of simpler associative mechanisms that underlie many theories of animallearning. In this study, human participants were trained on a five-pair TI problem (A⫹B⫺, B⫹C⫺, C⫹D⫺,D⫹E⫺, E⫹F⫺) and, unlike in previous human TI studies, were prevented from becoming explicitlyaware of the logical hierarchy, so they could not employ logical reasoning. They were then tested withthree problems: B versus D, B versus E, and C versus E. Participants only reliably chose B over E, whereasthe other test conditions yielded chance performance. This result is inconsistent with the use of logicalreasoning and is instead consistent with an account developed to explain earlier TI studies with rats thatfound the same pattern of results. In this account, choice performance is based on differential associa-tive strengths across the stimulus items that develop over training, despite equal overt reinforcement.IMPLICIT TRANSITIVE INFERENCE 743ing supported an alternative account that is consistentwith the observed pattern of results (Frank et al., 2003).The model suggested that differential associative strengthsaccrue across B and E, despite equal overt reinforcement(Figure 1). Although this finding contradicts the perva-sive assumption that equal overt reinforcement impliesequal underlying associative strengths, it follows natu-rally from basic learning mechanisms that were imple-mented in our model.1After training on the TI paradigm,the model developed a net positive association to B anda net negative association to E. This difference was suf-ficient to induce the model to reliably choose B over Eat test. The smaller difference between B and D valuesexplains inferior performance in the BD test case.The above reasoning suggests that TI-like behavior inanimals can be accounted for without invoking the use oflogical strategies. Thus, humans should also performwell in TI-like tasks without having to rely on explicitlogical reasoning. To test this idea, Greene, Spellman,Dusek, Eichenbaum, and Levy (2001) trained humanparticipants on the four-pair problem [AB, BC, CD, DE],using a training protocol similar to that used in rats. Ver-bal strategies were limited by using unfamiliar visualstimuli (Japanese hiragana characters). On the BD test,participants successfully chose B over D. It was con-cluded that explicit awareness was not necessary forTI-like behavior in humans. However, several partici-pants did indeed become aware of the hierarchy as train-ing progressed. Although performance was not corre-lated with postexperimental measures of awareness, thepossibility could not be excluded that some participantswere more aware than they reported. Furthermore, thesame ordering of hiragana