Mini-reviewTransitive inference in non-human animals: An empirical and theoretical analysis
Introduction
For thousands of years, the transitive inference (TI) problem has been one of the hallmarks of human logical deductive reasoning. This task, known to the ancient Greeks, and actually one the milestones of Aristotelian logic, was first introduced into modern psychology by Burt, 1911, Burt, 1919a, Burt, 1919b in order to evaluate the reasoning abilities of young children. Similarly, Piaget (1928) became interested in syllogisms as a means to understand the development of basic cognitive abilities.
As an illustration, suppose you are given the following propositions: “David is taller than John” and “John is taller than Peter”. Afterwards, you are asked “Who is taller, David or Peter?” The answer to this question is quite obvious despite the fact that this information was not directly presented. This simple task is a verbal instantiation of the TI task and the verbal report “David” (in the case above) is evidence for the TI ability. Although most human adults readily solve such syllogisms, the ability of children and non-human animals to solve this kind of problem was, and in some instances still is, questioned. For example, in Piaget, 1928, Piaget, 1955, Piaget, 1970, the TI competence emerges only with the concrete operational stage, which presumably precludes children younger than about 7 years old from a correct resolution of these tasks. Implicit in this position is the assumption that only after the acquisition of the rules of logic will a child correctly solve such syllogisms.
Formally, TI can be defined as a form of reasoning in which, given preliminary information (the premises), the subject deduces a logical conclusion. In general, a relation R between any two objects “a” and “c”, aRc, is said to be transitive if, given aRb and bRc, it follows that aRc. In a word, the ordinal relation between two elements must be inferred from premises that establish the relations of those two elements to a third (e.g., Halford, 1984). Given this definition, it should come as no surprise that TI has long been regarded as a hallmark of human cognitive abilities. Its apparent reliance on the rules of formal logic and its usual verbal implementation helped foster this somewhat anthropomorphic position.
It was in this long-established environment in which reasoning was seen as a general ability to correctly manipulate propositions according to the rules of logic that the question of whether non-human animals are able to correctly solve TI tasks was first raised. Needless to say, the question itself was at odds with the dominant theoretical standards. This scenario, however, was dramatically changed by a seminal paper by Bryant and Trabasso (1971). Using a semi-verbal instantiation of the TI task, they showed that failures of TI performance in young children reflected deficits of memory rather than deficits of logic or of any heuristic. Children were trained with pairs of rods of varying lengths and color, although only color was informative (the same length was visible for all rods). On each trial, children were presented with a pair or rods: A and B, B and C, C and D, or D and E and were asked which one was bigger or smaller. For example, red might be bigger than blue, blue might be bigger than green, and so forth. After learning the premises on a trial-and-error basis, children faced critical tests in which B and D were presented. The finding was that when children were tested only after they had clearly memorized the premises, they were indeed capable of TI, including the youngest, 4-year-olds (see also Riley and Trabasso, 1974). The ability to solve such syllogisms previous to the development of the cognitive abilities thought to sustain such performance strongly suggested that TI might be based on simpler mechanisms than previously acknowledged. Since then, the logical account fell out of favor and most research seems to support a mental model approach in humans (e.g., Byrne and Johnson-Laird, 1989, Carreiras and Santamaria, 1997; for details, see Section 4.1. below). Importantly, the door for the provocative hypothesis that non-human animals might be capable of TI was opened.
Since Bryant and Trabasso's (1971) paper, evidence for TI in a variety of species has steadily accumulated. The first to demonstrate TI in non-humans were McGonigle and Chalmers (1977) with squirrel monkeys, but after their demonstration many others followed: Boysen et al. (1993) and Gillan (1981) with chimpanzees; Buckmaster et al. (2004), McGonigle and Chalmers, 1977, McGonigle and Chalmers, 1992, Rapp et al. (1996), and Treichler and Van Tilburg (1996) with monkeys; Davis (1992b), Dusek and Eichenbaum (1997), Roberts and Phelps (1994), and Van Elzakker et al. (2003) with rats; Lazareva and Wasserman (2006), Siemann et al. (1996b), Steirn et al. (1995), von Fersen et al. (1991), Weaver et al. (1997), and Wynne (1997) with pigeons; Bond et al. (2003), and Paz-y-Miño et al. (2004) with pinyon jays; Bond et al. (2003) with scrub-jays; Lazareva et al. (2004) with hooded crows; and Grosenick et al. (2007) with fish (Astatotilapia burtoni).
The ability of non-human animals to solve transitive syllogisms may have an important adaptive value (e.g., Wynne, 1995). Rank estimation in social animals provide a good example (e.g., Cheney and Seyfarth, 1986, Cheney and Seyfarth, 1990). In species in which dominance is not evident from physical traits, an animal incapable of TI would face a combinatorial explosion from having to engage in potentially dangerous interactions with every single member of the group. For example, if three items have to be ranked, the three possible pairs have to be experienced; if six items have to be ranked, the 15 possible pairs have to be experienced, and so forth.
Suppose a new member joins a social group. One way to estimate rank is for each member of the group to interact with the newcomer. A more economical strategy would be to observe the newcomer's interactions with some members of the group and, based on the previous knowledge of the existing members’ rank, estimate the relative rank of the newcomer (von Fersen et al., 1991). Field observations suggest this is indeed the case (e.g., Altmman, 1962) and laboratory studies seem to corroborate such an assertion. For example, Paz-y-Miño et al. (2004) showed such an effect with pinyon jays (for examples with fish and hens, see Grosenick et al., 2007; and Hogue et al., 1996, respectively). Furthermore, the less social but closely related western scrub jays exhibit less transitive behavior (Bond et al., 2003). Whether or not this ability depends on the complexity of the animals’ social system is still uncertain, despite suppositions that such complexity might have driven the evolution of several cognitive abilities (e.g., Jolly, 1966, Kummer et al., 1997, Paz-y-Miño et al., 2004, Shettleworth, 2004).
In this paper, I review and analyze TI data in non-human animals, focusing on the proximal mechanisms proposed to explain this ability. I start by describing the tasks customarily used in TI studies with non-human animals, followed by the typical empirical findings. I analyze the results obtained with these tasks, focusing not only on the TI test itself but also on some interesting effects observed during training. Next, the models that have been proposed to explain TI in non-human animals are presented and analyzed. Of particular interest is the fit between the predictions of each model and the empirical findings, but careful attention will also be given to the models’ theoretical robustness. I end by shedding some light on what seem to be promising lines of research.
Section snippets
The transitive inference tasks
Most research on TI in non-human animals has used the so-called n-term series task. This task consists of the presentation of successive pairs of stimuli. Originally developed for children by Bryant and Trabasso (1971), it was modified into a fully non-verbal version by McGonigle and Chalmers (1977) in a well-known study with squirrel monkeys. In its simplest form, the task involves five different stimuli. Fig. 1 presents a schematic of the task.
Each pair represents a simultaneous
Evidence for transitive inference in non-human animals
Most studies on TI in non-human animals have yielded a relatively consistent pattern of findings within and across species. I start by characterizing the evidence for TI (performance at test) and then analyze training performance. I end this section by summarizing studies using what have been termed circular series. This will, in turn, allow a clearer understanding of the proposed explanatory models that heavily rely on training features.
Models of transitive inference
Of the several models proposed to explain TI, some are qualitative but most are quantitative in nature; some are clearly cognitive, using concepts such as mental representations and mental lines, but others are more behaviorally oriented focusing on such things as reinforcement histories and relative frequency of past events.
Directions for future research
Currently, both empirically and theoretically oriented questions remain unanswered. For instance, it has been implicitly assumed by most researchers that the transitive test after intermixed and sequential training taps the same TI-like ability. This assumption is based on the fact that such a test usually yields similar preferences. In addition, the ability of reinforcement-based, configural-cue models to predict animals’ performance both with intermixed and sequential training strengthened
Concluding remarks
TI has been demonstrated in a variety of different species. Using series of different lengths, different reinforcement contingencies, different sensory modalities, different training regimens, etc., the published evidence establishes TI in non-human animals as a reliable phenomenon. Furthermore, training and test data obtained with non-human animals closely parallels the typical findings obtained with humans: preference for the transitive alternative, the serial position effect, and the SDE
Acknowledgement
I thank John Capaldi, Jacky Emmerton, and George Hollich for comments on a earlier version of the paper. I am particularly grateful to Peter Urcuioli for his encouragement, guidance, and many critical readings.
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