Transitive inference

Such a type of reasoning as transitive inference (TI) allows us to easily reach the conclusion that, say, A is bigger than C if A is bigger than B, and B is bigger than C without having to see A and C side by side. The case of transitive inference is an example of a more general dispute between proponents of associative accounts and advocates of more cognitive account of animal behaviour (Allen, 2004).

Experimental procedure for studying transitivity is based on the technique of matching-to-sample (MTS) that was described in Chapter 14. When a subject is taught to select stimulus B in the presence of stimulus A and to select stimulus C in the present of B, it is likely that the subject also will select A in the presence of B (symmetry), B in the presence of C (symmetry), C in the presence of A (transitivity), and A in the presence of C (combined symmetry and transitivity, or equivalence) without further training. When this occurs, the stimuli are said to participate Roche et al., 1997 (Roche and Barnes, 1997). Animal versions of experimental schemes is derived from the original Piagetian version of the 5-element task (Piaget, 1952) designed to test transitive inference in young human children. In that version, symbols or colours were paired with different length rods.

In experiments of Gillan (1981), chimpanzees first were trained to find food in five containers, A, B, C, D, and E, each of which had a different colour. Containers were presented to the animals in pairs in accordance with the following schedule: A+B-, B+C-, C+D-, D+E-, where + denotes the container with food. The containers were changed by their places irregularly so that the discrimination could be solved only on the basis of colour. After a number of trials the subjects persistently preferred A to B, B to C, C to D, and D to E. To examine whether these relationships can be combined to lead a novel inference, Gillan then gave test sessions that included, for the first time, the pair B and D. If apes are capable of transitive inference, then combining the knowledge that B is preferred to C with the knowledge that C is preferred to D should lead to the conclusion that B is preferred to D. One chimpanzee, Sadie, performed perfectly on this test choosing B in preference to D on all 12 tests trials. Although the results for the other two chimpanzees were not so good, the success of Sadie shows that at least one chimpanzee can solve transitive inference problem.

Using the arbitrary MTS procedure, Schusterman and Kastak (1993) established that the California Sea lion (a female named Rio), could relate stimulus pairs AB and BC with specific reinforcement contingencies. To obtain reinforcement (a piece of fish), Rio made a choice by stickling her nose into one of the two boxes containing a discriminative stimuli. Rio was trained to select B comparison conditionally upon presentation of A samples and to select C comparison conditionally upon presentation of B samples, for each of 30 potential classes. Rio could immediately extend these relations without further training to stimulus pairs BA and CB (symmetry), AC (transitivity), and CA (equivalence). Ultimately, Rio had formed 30 three-member sets of stimuli, which were mutually substitutable within a matching-to-sample procedure. On another set of experiments with Rio, Schusterman and Kastak (1998) tested whether the discriminative function acquired in the MTS procedure by one member of an equivalence class transfers immediately and completely to the two other members of that class in a novel context. That is, if one member (A) of an equivalence class (ABC) becomes discriminative for a response, do the other members (B and C) also become discriminative for that same response? For instance, in one experiment two classes (numbered 1 and 2), each consisting of three members (A, B and C) were tested in a simple discrimination. The subject initially receives one simple discrimination pitting the B member of class 1 (B1) against the B member of class 2 (B2). If she selects B2 rather than B1, establishing B2 as the S+ and B1 as the S-, will she then select A2 rather than A1, when these stimuli are first presented as alternative choices? Will she also select C2 rather than C1 when they are also presented as alternative choices? In 28 of 30 tests, the sea lion immediately transferred the discriminative function acquired by one member of an equivalence class to the remaining members of that class. The elaborated relational concept, that of generalised identity matching was re-tested after ten years. Rio immediately and reliably applied the previously established identity concept to familiar and novel sets of matching problems (Reichmuth Kastak and Schusterman, 2002).

The use of the similar method has allowed suggesting transitive inference in pigeons (Fersen and Lea, 1990), squirrel monkeys (McGonigle and Chalmers, 1992), hooded crows (Zorina, 1997; Lazareva et al., 2004), and several other species (for detailed analysis see: Pearce, 2000).