## Inferential Reasoning Transitivity

The use of transitive inference has received much research attention. Although human studies on transitivity (see Halford, Chap. 22) have often used stimuli that vary systematically and naturally along a quantitative dimension such as height (e.g., Piaget, 1952), most studies with primates have used so-called associative transitivity. This consists of presenting subjects with pairs of arbitrary stimuli and differentially reinforcing one of the stimulus of the pair, thereby creating different values. For instance, the red cup is always reinforced when presented with the blue cup, whereas the blue cup is always reinforced when presented with the yellow cup, and so on. Once the initial pairs are trained, subjects are presented with pairs of stimuli that have not been paired before, for instance, red versus yellow cup.

There is ample evidence showing that primates can make transitive inferences when subjects are presented with novel pairs (D'Amato et al., 1985; D'Amato & Colombo, 1988; Gillan 1981; Boysen et al., 1 993). This includes cases in which subjects have been trained with more than three stimuli. This is important because the most interesting cases are those that involve intermediate stimuli - that is, stimuli that are not the first or the last of the sequence, because those are always or never reinforced, respectively. D'Amato and Colombo (1988) trained capuchin monkeys to touch five arbitrary items in a specified order (labeled A, B, C, D, and E). After they had mastered this task they were presented with novel pairs. Of particular importance were the internal pairs B-C, C-D, and B-D. The B-D comparison was especially important because these two items were both internal to the series and were nonadjacent to one another in the previous training. Subjects ordered these three internal pairs correctly 81% to 88% of the time, well above chance. When presented with triplets from which they were to choose the highest item, they ordered the internal triplet B-C-D correctly 94% of the time, also well above chance. This finding essentially replicates, with even stronger results, the findings of McGonigle and Chalmers (1977) with squirrel monkeys. These authors also found evidence for a symbolic distance effect - the farther apart two items, the more successful the subjects, presumably because the items were easier to distinguish.

One open question is, What is the mechanism responsible for this performance? Two mechanisms have been postulated - the associative mechanisms based on responding to the differential reinforcement and associative strength of the stimuli, and the relational or linear mechanism based on creating a mental order of the stimuli. Bond, Kamil, and Balda (2003) argued that, under an associative mechanism, errors increase at the end of the sequence, whereas latencies should be unaffected regardless of the position of the items. In contrast, the relational mechanism predicts that accuracy will remain unchanged, whereas the latency to respond will be affected. First, subjects' latency to respond to the first item of a pair increased as that item moved down the series: They responded most quickly to pairs in which the first item was A, then for pairs in which the first item was B, then C, then D. The implication is that each time they are presented with a pair, the subjects are mentally reconstructing the entire five-item series (D'Amato & Colombo, 1988). Second, animals responded most quickly to the second item of a pair for pairs with adjacent items (e.g., A-B, C-D, etc.), then for pairs separated by one gap (e.g., A-C, C-E, etc.), then for pairs separated by two gaps (i.e., A-D, B-E), and they were slowest on the second item when the gap was three (A-E). Again, the implication is that subjects are going through the entire series mentally on every trial. Swartz, Chen, and Terrace (1991) essentially replicated these results - both in terms of ordinal judgments and in terms of reaction times - for rhesus macaques.

Although these results are quite convincing, D'Amato and Colombo (1989) pointed out that the results of this study are compatible with an associative chain interpretation in which each item simply serves as a discriminative stimulus evoking the next item, obviating the need for some representation of serial order. To investigate whether capuchin monkeys were also associating a specific serial position with each item in the associative chain, D'Amato and Colombo (1989) used a procedure that essentially broke the chain. Using monkeys who had already learned the ABCDE sequence, on some trials they introduced a "wild card" item at a particular point in the sequence (e.g., ABCXE). This was a novel item that had never been used as part of the training and therefore had no associations with any other items. These investigators found that no matter the position in which the wild card item appeared, subjects treated it in a manner similar to the item it replaced at above-chance levels, touching it at the appropriate place in the sequence approximately 60% of the time. They performed just as well with sequences containing two wild card items. Consequently, D'Amato and Colombo argued that the monkeys in this study, and presumably in previous studies, were operat ing with something more than an associative chain; they were operating with some mentally represented sequence of items in which the ordinal position of each item was essential information.