The transitive inference task was developed by Piaget (1928) as a tool for the assessment of cognitive development in children. A child is said to make a transitive inference when, based on a set of relational propositions, s/he infers a relation that has not been provided explicitly. Such relations are said to have emergent properties because they were not trained. An example of such a transitive inference is, if a child is told that an object A is larger than B, and that B is larger than C, s/he may infer than A is larger than C. If such an inference is made, the presumption has been that B serves to mediate the emergent relation between A and C. Although there is some disagreement about the age and level of development at which transitive inference appears in children (see Bryant & Trabasso, 1971), the transitive inference task remains an important index of relative cognitive development in humans.

Interest in the cognitive capacity of animals has lead to the design of procedures that have attempted to translate tests of cognitive development into a form that can be used with nonverbal organisms. For example, Doré (1986) has examined object permanence in cats and Woodruff, Kennel, and Premack (1978) have looked at conservation of various materials in a chimpanzee..

The strength of the transitive inference task, when it used with human s, is that it is presented in verbal form. Because the proposition, A is larger than B, is presented verbally, without regard to perceivable objects, the stimuli need have no absolute properties. Typically, they have only relational properties (i.e., the communication says nothing about the absolute size of A or B). However, its strength with humans is a disadvantage with (nonverbal) animals. If one were to present the propositions of a transitive inference task to an animal (e.g., A is better than B, and B is better than C), A would have some inherent value, as would B and C. On the test trial, one could compare directly, the inherent value of A to the inherent value of C. Thus, one could select A over C, without having to make an inference involving B. Thus, such a nonverbal form of the transitive inference task would defeat the purpose of the procedure.

McGonigle and Chalmers (1977) were the first to propose, as a solution to this problem, the five-term series with equal absolute value given to the two stimuli (i.e., the better-than stimulus and the worse-than stimulus) in each proposition. They suggested that five stimuli could be arranged in four propositions (simultaneous discriminations) that could maintain the appropriate logical relation 324among the stimuli, while avoiding differential absolute value for the stimuli in the test pair. For example, if responses to A are reinforced in the presence of B (A+B-), responses to B are reinforced in the presence of C (B+C-), responses to C are reinforced in the presence of D (C+D-), and responses to D are reinforced in the presence of E (D+E-), such training may establish the relational series A>B>C>D>E (see Table 1). Although responses to A are always reinforced (so A should be more preferred than all of the others) and responses to E are never reinforced (so E should be less preferred than all the others), responses to B, C, and D are all sometimes reinforced and sometimes not. Furthermore, of these three stimuli, B and D were never experienced together in training and thus, they can serve as an appropriate test pair. If, as a result of the above training, an organism selects B over D, it has been proposed that relational learning has occurred (Davis, 1992). (For descriptive purposes, such a result will be viewed as an empirical finding of transitive inference even when relational learning is not implied.) Using this and similar procedures, evidence for transitive inference (in the form of test pair transfer performance) has been found in a number of nonverbal species, including chimpanzees (Gillan, 1981), monkeys (McGonigle & Chalmers, 1977), rats (Davis, 1992), and pigeons (Fersen, Wynne, Delius, & Staddon, 1991; Steirn, Weaver, & Zentall, 1995; Weaver, Steirn, & Zentall, in press; Wynne, 1995).