Effect of stimulus orderability and reinforcement history on transitive responding in pigeons

Hippocampal Pallium Lesion Impairs Transitive Inference in Goldfish

Transitive inference, a process that involves drawing logical conclusions based on preliminary information, is considered a cornerstone of human deductive reasoning. Furthermore, transitive inference is a clear instance of representational flexibility as it implies the novel expression of learned information. In mammals and birds, both episodic memory and transitive inference critically depend on the integrity of the hippocampus. Comparative neurobiological evidence indicates that a hippocampus homologue can also be found in the telencephalic pallium of teleost fish. Here, we investigated whether goldfish demonstrate inferential behavior in a standard transitive inference task, and whether the hippocampal pallium of goldfish, akin to the hippocampus in mammals and birds, plays a role in transitive responding. We trained goldfish with hippocampal pallium lesions and sham-operated controls on a series of overlapping two-item visual premise pairs: A+B-, B+C-, C+D-, D+E-. The sham-operated animals readily learned the premise pair discriminations and responded transitively during the crucial test involving a novel pair of nonadjacent elements (B vs. D). However, hippocampal pallium-lesioned goldfish were impaired in the critical transitive inference test, although they successfully learned to discriminate the premise pairs. These findings suggest that a relational memory function, which supports the novel expression of learned information, could be a primitive feature of the vertebrate hippocampus. Such outcome contributes significantly to the ongoing debate regarding the evolutionary origins of episodic memory in vertebrates.

Honey bees rely on associative stimulus strength after training on an olfactory transitive inference task

Transitive inference, the ability to establish hierarchical relationships between stimuli, is typically tested by training with premise pairs (e.g., A + B-, B + C-, C + D-, D + E-), which establishes a stimulus hierarchy (A > B > C > D > E). When subjects are tested with non-adjacent stimuli (e.g., B vs. D), a preference for B indicates transitive inference, while no preference indicates decisions based on stimulus associative strength, as B and D are equally reinforced. Previous studies with bees and wasps, conducted in an operant context, have shown conflicting results. However, this context allows free movement and the possibility to avoid non-reinforced options, thus reducing the number of non-reinforced trials. To address this, we examined whether honey bees could perform transitive inference using a Pavlovian protocol that fully controls reinforcement. We conditioned bees with five odorants, either forward-or backward-paired with a sucrose solution, across four discrimination tasks. In all experiments, bees showed no preference for B over D, choosing equally between them, regardless of the training schedule. Our results show that bees' choices were primarily influenced by stimulus associative strength and a recency effect, with greater weight given to the most recent reinforced or non-reinforced stimulus. We discuss these findings in the context of honey bee memory, suggesting that memory constraints may limit cognitive solutions to transitive inference tasks in bees.

Transitive reasoning in the adult domestic hen in a six-term series task

Transitive inference (TI) is a disjunctive syllogism that allows an individual to indirectly infer a relationship between two components, by knowing their respective relationship to a third component (if A > B and B > C, then A > C). The common procedure is the 5-term series task, in which individuals are tested on indirect, unlearned relations. Few bird species have been tested for TI to date, which limits our knowledge of the phylogenetic spread of such reasoning ability. Here we tested TI in adult laying hens using a more solid methodology, the 6-term series task, which has not been tested in poultry so far. Six hens were trained to learn direct relationships in a sequence of six arbitrary items (A > B > C > D > E > F) in a hybrid training procedure. Then, 12 testing sessions were run, comprising 3 non-rewarded inference trials each: BD, BE, and CE. All subjects showed TI within 12 inference trials and were capable of TI whatever the relative distance between the items in the series. We found that TI performance was not impacted by the reinforcement ratios of the items for most individuals, making it harder to support a purely associative-based resolution of the task. We suggest that TI is based on the same cognitive processes in poultry (Galloanserae) than in modern flying birds (Neoaves), and that the cognitive strategy to solve the task might be driven mainly by individual parameters within species. These results contribute to a better understanding of transitive inference processes in birds.

Crows "count" the number of self-generated vocalizations

Producing a specific number of vocalizations with purpose requires a sophisticated combination of numerical abilities and vocal control. Whether this capacity exists in animals other than humans is yet unknown. We show that crows can flexibly produce variable numbers of one to four vocalizations in response to arbitrary cues associated with numerical values. The acoustic features of the first vocalization of a sequence were predictive of the total number of vocalizations, indicating a planning process. Moreover, the acoustic features of vocal units predicted their order in the sequence and could be used to read out counting errors during vocal production.

In the absence of extensive initial training, cleaner wrasse Labroides dimidiatus fail a transitive inference task

Transitive inference (TI) is a reasoning capacity that allows individuals to deduce unknown pair relationships from previous knowledge of other pair relationships. Its occurrence in a wide range of animals, including insects, has been linked to their ecological needs. Thus, TI should be absent in species that do not rely on such inferences in their natural lives. We hypothesized that the latter applies to the cleaner wrasse Labroides dimidiatus and tested this with 19 individuals using a five-term series (A > B > C > D > E) experiment. Cleaners first learned to prefer a food-rewarding plate (+) over a non-rewarding plate (-) in four plate pairs that imply a hierarchy from plate A to plate E (A+B-, B+C-, C+D-, D+E-), with the learning order counterbalanced between subjects. We then tested for spontaneous preferences in the unknown pairs BD (transitive inference task) and AE (as a control for anchors), interspersed between trials involving a mix of all known adjacent pairs. The cleaners systematically preferred A over E and showed good performance for A+B- and D+E- trials. Conversely, cleaners did not prefer B over D. These results were unaffected by the reinforcement history, but the order of learning of the different pairs of plates had a main impact on the remembrance of the initial training pairs. Overall, cleaners performed randomly in B+C- and C+D- trials. Thus, a memory constraint may have prevented subjects from applying TI. Indeed, a parallel study on cleaner wrasse provided positive evidence for TI but was achieved following extensive training on the non-adjacent pairs which may have over-ridden the ecological relevance of the task.

Individual differences could explain the failure in transitive inference formation in pigeons using probabilistic reinforcement

In propositional logic, it is stated that "for if A is predicated for every B, and B for every C, A must necessarily be predicated of every C". Following a similar logical process, it can be said that If A > B and B > C, then A > C, this is called transitive inference (TI). Piaget developed a verbal task to evaluate TI in children. Subsequent studies adapted this task for animals using a conditioned discrimination between five-terms sequence of stimuli A + B-, B + C-, C + D-, and D + E-. If subjects prefer B over D during test, it is assumed that TI has occurred. In this experiment, we analyzed the effects of task complexity on TI by using a five-terms sequence of stimuli associated with probabilistic outcomes during training, in pigeons. Thus, both stimuli are reinforced in each pair but with different probability, 0.8 for + stimulus and 0.2 for the-stimulus. We found that performance during C + D- pair is impaired and preference in the test pair BD is affected. However, this impairment is dependent on individual differences in performance in C + D- pair. We compare our findings with previous research and conclude that Pavlovian mechanisms, as well as ordering of stimuli, can account for our findings.

Probabilistic reinforcement precludes transitive inference: A preliminary study

In the basic verbal task from Piaget, when a relation of the form if A > B and B > C is given, a logical inference A > C is expected. This process is called transitive inference (TI). The adapted version for animals involves the presentation of a simultaneous discrimination between stimuli pairs. In this way, when A+B-, B+C-, C+D-, D+E- is trained, a B>D preference is expected, assuming that if A>B>C>D>E, then B>D. This effect has been widely reported using several procedures and different species. In the current experiment TI was evaluated employing probabilistic reinforcement. Thus, for the positive stimuli a .7 probability was administered and for the negative stimuli a .3 probability was administered. Under this arrangement the relation A>B>C>D>E is still allowed, but TI becomes more difficult. Five pigeons (Columba Livia) were exposed to the mentioned arrangement. Only one pigeon reached the criterion in C+D- discrimination, whereas the remaining did not. Only the one who successfully solved C+D- was capable of learning TI, whereas the others were not. Additionally, it was found that correct response ratios did not predict BD performance. Consequently, probabilistic reinforcement disrupted TI, but some positional ordering was retained in the test. The results suggest that TI might be affected by associative strength but also by the positional ordering of the stimuli. The discussion addresses the two main accounts of TI: the associative account and the ordinal representation account.

Thinking about order: a review of common processing of magnitude and learned orders in animals

Rich behavioral and neurobiological evidence suggests cognitive and neural overlap in how quantitatively comparable dimensions such as quantity, time, and space are processed in humans and animals. While magnitude domains such as physical magnitude, time, and space represent information that can be quantitatively compared (4 "is half of" 8), they also represent information that can be organized ordinally (1→2→3→4). Recent evidence suggests that the common representations seen across physical magnitude, time, and space domains in humans may be due to their common ordinal features rather than their common quantitative features, as these common representations appear to extend beyond magnitude domains to include learned orders. In this review, we bring together separate lines of research on multiple ordinal domains including magnitude-based and learned orders in animals to explore the extent to which there is support for a common cognitive process underlying ordinal processing. Animals show similarities in performance patterns across natural quantitatively comparable ordered domains (physical magnitude, time, space, dominance) and learned orders (acquired through transitive inference or simultaneous chaining). Additionally, they show transfer and interference across tasks within and between ordinal domains that support the theory of a common ordinal representation across domains. This review provides some support for the development of a unified theory of ordinality and suggests areas for future research to better characterize the extent to which there are commonalities in cognitive processing of ordinal information generally.

Hippocampal and medial prefrontal cortices encode structural task representations following progressive and interleaved training schedules

Memory generalisations may be underpinned by either encoding- or retrieval-based generalisation mechanisms and different training schedules may bias some learners to favour one of these mechanisms over the other. We used a transitive inference task to investigate whether generalisation is influenced by progressive vs randomly interleaved training, and overnight consolidation. On consecutive days, participants learnt pairwise discriminations from two transitive hierarchies before being tested during fMRI. Inference performance was consistently better following progressive training, and for pairs further apart in the transitive hierarchy. BOLD pattern similarity correlated with hierarchical distances in the left hippocampus (HIP) and medial prefrontal cortex (MPFC) following both training schedules. These results are consistent with the use of structural representations that directly encode hierarchical relationships between task features. However, such effects were only observed in the MPFC for recently learnt relationships. Furthermore, the MPFC appeared to maintain structural representations in participants who performed at chance on the inference task. We conclude that humans preferentially employ encoding-based mechanisms to store map-like relational codes that can be used for memory generalisation. These codes are expressed in the HIP and MPFC following both progressive and interleaved training but are not sufficient for accurate inference.

Influence of Rule- and Reward-based Strategies on Inferences of Serial Order by Monkeys

Knowledge of transitive relationships between items can contribute to learning the order of a set of stimuli from pairwise comparisons. However, cognitive mechanisms of transitive inferences based on rank order remain unclear, as are relative contributions of reward associations and rule-based inference. To explore these issues, we created a conflict between rule- and reward-based learning during a serial ordering task. Rhesus macaques learned two lists, each containing five stimuli that were trained exclusively with adjacent pairs. Selection of the higher-ranked item resulted in rewards. "Small reward" lists yielded two drops of fluid reward, whereas "large reward" lists yielded five drops. Following training of adjacent pairs, monkeys were tested on novels pairs. One item was selected from each list, such that a ranking rule could conflict with preferences for large rewards. Differences between the corresponding reward magnitudes had a strong influence on accuracy, but we also observed a symbolic distance effect. That provided evidence of a rule-based influence on decisions. RT comparisons suggested a conflict between rule- and reward-based processes. We conclude that performance reflects the contributions of two strategies and that a model-based strategy is employed in the face of a strong countervailing reward incentive.

Positional inference in rhesus macaques

Understanding how organisms make transitive inferences is critical to understanding their general ability to learn serial relationships. In this context, transitive inference (TI) can be understood as a specific heuristic that applies broadly to many different serial learning tasks, which have been the focus of hundreds of studies involving dozens of species. In the present study, monkeys learned the order of 7-item lists of photographic stimuli by trial and error, and were then tested on "derived" lists. These derived test lists combined stimuli from multiple training lists in ambiguous ways, sometimes changing their order relative to training. We found that subjects displayed strong preferences when presented with novel test pairs, even when those pairs were drawn from different training lists. These preferences were helpful when test pairs had an ordering congruent with their ranks during training, but yielded consistently below-chance performance when pairs had an incongruent order relative to training. This behavior can be explained by the joint contributions of transitive inference and another heuristic that we refer to as "positional inference." Positional inferences play a complementary role to transitive inferences in facilitating choices between novel pairs of stimuli. The theoretical framework that best explains both transitive and positional inferences is a spatial model that represents both the position of each stimulus and its uncertainty. A computational implementation of this framework yields accurate predictions about both correct responses and errors on derived lists.

Transitive inference in cleaner wrasses (Labroides dimidiatus)

Transitive inference (TI) is the ability to infer unknown relationships from previous information. To test TI in non-human animals, transitive responding has been examined in a TI task where non-adjacent pairs were presented after premise pair training. Some mammals, birds and paper wasps can pass TI tasks. Although previous studies showed that some fish are capable of TI in the social context, it remains unclear whether fish can pass TI task. Here, we conducted a TI task in cleaner wrasses (Labroides dimidiatus), which interact with various client fishes and conspecifics. Because they make decisions based on previous direct and indirect interactions in the context of cleaning interactions, we predicted that the ability of TI is beneficial for cleaner fish. Four tested fish were trained with four pairs of visual stimuli in a 5-term series: A-B+, B-C+, C-D+, and D-E+ (plus and minus denote rewards and non-rewards, respectively). After training, a novel pair, BD (BD test), was presented wherein the fish chose D more frequently than B. In contrast, reinforcement history did not predict the choice D. Our results suggest that cleaner fish passed the TI task, similar to mammals and birds. Although the mechanism underlying transitive responding in cleaner fish remains unclear, this work contributes to understanding cognitive abilities in fish.

Associative models fail to characterize transitive inference performance in rhesus monkeys (Macaca mulatta)

It has been suggested that non-verbal transitive inference (if A > B and B > C, then A > C) can be accounted for by associative models. However, little is known about the applicability of such models to primate data. In Experiment 1, we tested the fit of two associative models to primate data from both sequential training, in which the training pairs were presented in a backward order, and simultaneous training, in which all training pairs are presented intermixed from the beginning. We found that the models provided an equally poor fit for both sequential and simultaneous training presentations, contrary to the case with data from pigeons. The models were also unable to predict the robust symbolic distance effects characteristic of primate transitive choices. In Experiment 2, we used the models to fit a list-linking design in which two seven-item transitive lists were first trained independently (A > B…. > F > G and H > I …. > M > N) then combined via a linking pair (G+ H-) into a single, 14-item list. The model produced accurate predictions for between-list pairs, but did not predict transitive responses for within-list pairs from list 2. Overall, our results support research indicating that associative strength does not adequately account for the behavior of primates in transitive inference tasks. The results also suggest that transitive choices may result from different processes, or different weighting of multiple processes, across species.

Transitive inference in Polistes paper wasps

Transitive inference (TI) is a form of logical reasoning that involves using known relationships to infer unknown relationships (A > B; B > C; then A > C). TI has been found in a wide range of vertebrates but not in insects. Here, we test whether Polistes dominula and Polistes metricus paper wasps can solve a TI problem. Wasps were trained to discriminate between five elements in series (A₀B-, B₀C-, C₀D-, D₀E-), then tested on novel, untrained pairs (B versus D). Consistent with TI, wasps chose B more frequently than D. Wasps organized the trained stimuli into an implicit hierarchy and used TI to choose between untrained pairs. Species that form social hierarchies like Polistes may be predisposed to spontaneously organize information along a common underlying dimension. This work contributes to a growing body of evidence that the miniature nervous system of insects does not limit sophisticated behaviours.

Mutations in neuroligin-3 in male mice impact behavioral flexibility but not relational memory in a touchscreen test of visual transitive inference

Cognitive dysfunction including disrupted behavioral flexibility is central to neurodevelopmental disorders such as Autism Spectrum Disorder (ASD). A cognitive measure that assesses relational memory, and the ability to flexibly assimilate and transfer learned information is transitive inference. Transitive inference is highly conserved across vertebrates and disrupted in cognitive disorders. Here, we examined how mutations in the synaptic cell-adhesion molecule neuroligin-3 (Nlgn3) that have been documented in ASD impact relational memory and behavioral flexibility. We first refined a rodent touchscreen assay to measure visual transitive inference, then assessed two mouse models of Nlgn3 dysfunction (Nlgn3^−/y and Nlgn3^R451C). Deep analysis of touchscreen behavioral data at a trial level established we could measure trajectories in flexible responding and changes in processing speed as cognitive load increased. We show that gene mutations in Nlgn3 do not disrupt relational memory, but significantly impact flexible responding. Our study presents the first analysis of reaction times in a rodent transitive inference test, highlighting response latencies from the touchscreen system are useful indicators of processing demands or decision-making processes. These findings expand our understanding of how dysfunction of key components of synaptic signaling complexes impact distinct cognitive processes disrupted in neurodevelopmental disorders, and advance our approaches for dissecting rodent behavioral assays to provide greater insights into clinically relevant cognitive symptoms.

Discovering Implied Serial Order Through Model-Free and Model-Based Learning

Humans and animals can learn to order a list of items without relying on explicit spatial or temporal cues. To do so, they appear to make use of transitivity, a property of all ordered sets. Here, we summarize relevant research on the transitive inference (TI) paradigm and its relationship to learning the underlying order of an arbitrary set of items. We compare six computational models of TI performance, three of which are model-free (Q-learning, Value Transfer, and REMERGE) and three of which are model-based (RL-Elo, Sequential Monte Carlo, and Betasort). Our goal is to assess the ability of these models to produce empirically observed features of TI behavior. Model-based approaches perform better under a wider range of scenarios, but no single model explains the full scope of behaviors reported in the TI literature.

Transitive inference in pigeons may result from differential tendencies to reject the test stimuli acquired during training

In the five-term, transitive inference task used with animals, pigeons are trained on four simultaneous discrimination premise pairs: A + B -, B + C -, C + D -, D + E -. Typically, when tested with the BD pair, most pigeons show a transitive inference effect, choosing B over D. Two non-inferential hypotheses have been proposed to account for this effect but neither has been reliably supported by research. Here we test a third non-inferential hypothesis that the preference for B arises because the animals have not had as much experience with B - in the A + B - discrimination as they have had with the D - in the C + D - discrimination. To test this hypothesis we trained the Experimental Group with the A + B - discrimination in which, over trials, there were four possible A + stimuli that could appear. This was done to encourage the pigeons to learn to reject the B - stimulus. For the Control Group there was only one A + stimulus over trials, as is typically the case. We also varied the nature of the stimuli between groups, such that colors served as the stimuli for half of the pigeons, whereas flags of different counties served as stimuli for the remaining pigeons. In both stimulus conditions, for the Experiment Group, we found little preference for stimulus B over stimulus D, whereas for the Control Group we found the typical preference for stimulus B. Thus, we propose that it is not necessary to attribute the transitive inference effect to an inferential process.

Corrigendum: Transitive Inference Remains Despite Overtraining on Premise Pair C+D

[This corrects the article DOI: 10.3389/fpsyg.2018.01791.].

Transitive Inference Remains Despite Overtraining on Premise Pair C+D-

Transitive inference (TI) has been studied in humans and several animals such as rats, pigeons and fishes. Using different methods for training premises it has been shown that a non-trained relation between stimuli can be stablished, so that if A > B > C > D > E, then B > D. Despite the widely reported cases of TI, the specific mechanisms underlying this phenomenon remain under discussion. In the present experiment pigeons were trained in a TI procedure with four premises. After being exposed to all premises, the pigeons showed a consistent preference for B over D during the test. After overtraining C+D- alone, B was still preferred over D. However, the expected pattern of training performance (referred to as serial position effect) was distorted, whereas TI remained unaltered. The results are discussed regarding value transfer and reinforcement contingencies as possible mechanisms. We conclude that reinforcement contingencies can affect training performance without altering TI.

Inferential Learning of Serial Order of Perceptual Categories by Rhesus Monkeys (Macaca mulatta)

Category learning in animals is typically trained explicitly, in most instances by varying the exemplars of a single category in a matching-to-sample task. Here, we show that male rhesus macaques can learn categories by a transitive inference paradigm in which novel exemplars of five categories were presented throughout training. Instead of requiring decisions about a constant set of repetitively presented stimuli, we studied the macaque's ability to determine the relative order of multiple exemplars of particular stimuli that were rarely repeated. Ordinal decisions generalized both to novel stimuli and, as a consequence, to novel pairings. Thus, we showed that rhesus monkeys could learn to categorize on the basis of implied ordinal position, without prior matching-to-sample training, and that they could then make inferences about category order. Our results challenge the plausibility of association models of category learning and broaden the scope of the transitive inference paradigm.SIGNIFICANCE STATEMENT The cognitive abilities of nonhuman animals are of enduring interest to scientists and the general public because they blur the dividing line between human and nonhuman intelligence. Categorization and sequence learning are highly abstract cognitive abilities each in their own right. This study is the first to provide evidence that visual categories can be ordered serially by macaque monkeys using a behavioral paradigm that provides no explicit feedback about category or serial order. These results strongly challenge accounts of learning based on stimulus-response associations.

Pigeons and the Ambiguous-Cue Problem: A Riddle that Remains Unsolved

The ambiguous-cue task is composed of two-choice simultaneous discriminations involving three stimuli: positive (P), ambiguous (A), and negative (N). Two different trial types are presented: PA and NA. The ambiguous cue (A) served as an S- in PA trials, but as an S+ in NA trials. When using this procedure, it is typical to observe a less accurate performance in PA trials than in NA trials. This is called the ambiguous-cue effect. Recently, it was reported in starlings that the ambiguous-cue effect decreases when the stimuli are presented on an angled (120°) panel. The hypothesis is that the angled panel facilitates that the two cues from each discrimination are perceived as a compound, precluding value transfer via a second-order conditioning mechanism. In this experiment, we used pigeons and a flat panel. Nevertheless, our data were quite similar to the previous data in starlings. We conclude that the form of the panel cannot explain the ambiguous-cue effect. Several alternatives to be explored in future experiments are suggested. The riddle of the ambiguous-cue problem still remains unsolved.

Endpoint distinctiveness facilitates analogical mapping in pigeons

Analogical thinking necessitates mapping shared relations across two separate domains. We investigated whether pigeons could learn faster with ordinal mapping of relations across two physical dimensions (circle size & choice spatial position) relative to random mapping of these relations. Pigeons were trained to relate six circular samples of different sizes to horizontally positioned choice locations in a six alternative matching-to-sample task. Three pigeons were trained in a mapped condition in which circle size mapped directly onto choice spatial position. Three other pigeons were trained in a random condition in which the relations between size and choice position were arbitrarily assigned. The mapped group showed an advantage over the random group in acquiring this task. In a subsequent second phase, relations between the dimensions were ordinally reversed for the mapped group and re-randomized for the random group. There was no difference in how quickly matching accuracy re-emerged in the two groups, although the mapped group eventually performed more accurately. Analyses suggested this mapped advantage was likely due to endpoint distinctiveness and the benefits of proximity errors during choice responding rather than a conceptual or relational advantage attributable to the common or ordinal mapping of the two dimensions. This potential difficulty in mapping relations across dimensions may limit the pigeons' capacity for more advanced types of analogical reasoning. This article is part of a Special Issue entitled: Tribute to Tom Zentall.

European starlings unriddle the ambiguous-cue problem

The ambiguous-cue problem is deceptively simple. It involves two concurrently trained simultaneous discriminations (known as PA and NA trials), but only three stimuli. Stimulus A is common to both discriminations, but serves as non-reinforced stimulus (S-) on PA trials and as reinforced stimulus (S+) on NA trials. Typically, animals’ accuracy is lower on PA trials—the ambiguous-cue effect. We conducted two experiments with European starlings (Sturnus vulgaris) using Urcuioli and Michalek’s (2007, Psychon B Rev 14, 658–662) experimental manipulations as a springboard to test the predictions of two of the most important theoretical accounts of the effect: the interfering cue hypothesis and value transfer theory. Both experiments included two groups of birds, one trained with a regular ambiguous-cue problem (Group Continuous) and another trained with partial reinforcement on PA trials (Group PA-Partial). The experiments differed only in the number of sessions (18 vs. 36) and daily trials (360 vs. 60). As previously observed, we found faster acquisition on NA trials than on PA trials in both experiments, but by the end of training PA performance was surprisingly high, such that no ambiguous-cue effect was present in Group Continuous of either experiment. The effect was still present in both PA-Partial groups, but to a smaller degree than expected. These findings are inconsistent with the literature, in particular with the results of Urcuioli and Michalek (2007) with pigeons, and question the aforementioned theoretical accounts as complete explanations of the ambiguous-cue effect. In our view, to achieve such high levels of accuracy on PA trials, starlings must have attended to configural (i.e., contextual) cues, thus differentiating stimulus A when presented on PA trials from stimulus A when presented on NA trials. A post hoc simulation of a reinforcement-based configural model supported our assertion.

Effects of spatial training on transitive inference performance in humans and rhesus monkeys

It is often suggested that transitive inference (TI; if A > B and B > C, then A > C) involves mentally representing overlapping pairs of stimuli in a spatial series. However, there is little direct evidence to unequivocally determine the role of spatial representation in TI. We tested whether humans and rhesus monkeys use spatial representations in TI by training them to organize 7 images in a vertical spatial array. Then, we presented subjects with a TI task using these same images. The implied TI order was either congruent or incongruent with the order of the trained spatial array. Humans in the congruent condition learned premise pairs more quickly, and were faster and more accurate in critical probe tests, suggesting that the spatial arrangement of images learned during spatial training influenced subsequent TI performance. Monkeys first trained in the congruent condition also showed higher test trial accuracy when the spatial and inferred orders were congruent. These results directly support the hypothesis that humans solve TI problems by spatial organization, and suggest that this cognitive mechanism for inference may have ancient evolutionary roots.

Transitive inference by pigeons: does the geometric presentation of the stimuli make a difference?

In studies of transitive inference (TI), nonhuman animals are typically trained with the following 5-term task: A+B-, B+C-, C+D-, D+E- where the letters stand for arbitrary stimuli and [+] indicates that choice is reinforced and [-] indicates that choice is not reinforced. A TI effect is found when, given the untrained test pair BD, subjects choose B. TI effects have been found in many nonhuman species. Although reinforcement history has been posited as an account of the TI effect, it has failed to account for a variety of conditions under which TI effects have been found. A more cognitive account of TI is that organisms are able to form a representation of the series (A>B>C>D>E). In support of this hypothesis, Roberts and Phelps (Psychol Sci 5:368-374, 1994) found that presentation of the pairs of stimuli in a linear arrangement facilitated TI performance by rats, whereas presentation of the pairs of stimuli in a circular arrangement did not. Using methods adapted from Roberts and Phelps, we trained pigeons on either a linear or a circular arrangement of stimuli with the 5-term task. Results indicated that on the BD test pair, pigeons trained with a circular arrangement did not differ from those trained with a linear arrangement. Furthermore, we found that memory for training pairs was variable and was highly correlated with degree of TI. The results suggest that regardless of how pigeons are able to represent the stimuli, choice was not affected by the spatial arrangement of the stimuli during training.

Six-term transitive inference with pigeons: successive-pair training followed by mixed-pair training

In nonhuman animals, the transitive inference (TI) task typically involves training a series of four simultaneous discriminations involving, for example, arbitrary colors in which choice of one stimulus in each pair is reinforced [+] and choice of the other color is nonreinforced [-]. This can be represented as A+B-, B+C-, C+D-, D+E- and can be conceptualized as a series of linear relationships: A > B > C > D > E. After training, animals are tested on the untrained non-endpoint pair, BD. Preference for B over D is taken as evidence of TI and occurs because B is greater than D in the implied series. In the present study we trained pigeons using a novel training procedure-a hybrid of successive pair training (training one pair at a time) and mixed-pair training (training all pairs at once)-designed to overcome some of the limitations of earlier procedures. Using this hybrid procedure, we trained five premise pairs (A+B-, B+C-, C+D-, D+E-, and E+F-) which allowed us to test three untrained non-endpoint pairs (BD, CE, and BE). A significant TI effect was found for most subjects on at least two out of three test pairs. Different theories of TI are discussed. The results suggest that this hybrid training is an efficient procedure for establishing mixed-pair acquisition and a TI effect.

Transitive inference in jackdaws (Corvus monedula)

Transitive inference (TI) refers to the cognitive ability to derive relationships between items that have never been presented together before. TI could be a useful tool for individuals living in large social groups, as these are confronted with an increasing number of possible dyadic relationships between group members. Through TI, one could potentially identify rank relationships between group members and thereby avoid costly direct agonistic interactions. Jackdaws seem ideal candidates to test for the ability of TI as they live in relatively complex groups, in which such skills could be useful. We presently report the results of jackdaws in a touch screen experiment. Three individuals were trained to memorise an ordered sequence of five differently coloured squares (A-E), which were presented in four pairs consisting of two adjacent colours each (A/B, B/C, C/D, D/E). After reaching the pre-defined criteria in each single colour pair in a time comparable to other species, they were confronted with an unknown pair of two non-adjacent colours (B/D). The birds were able to identify the relationship according to the previously learned sequence by preferring B over D.

Cognitive mechanisms for transitive inference performance in rhesus monkeys: measuring the influence of associative strength and inferred order

If Ben is taller than Emily and Emily is taller than Dina, one can infer that Ben is taller than Dina. This process of inferring relations between stimuli based on shared relations with other stimuli is called transitive inference (TI). Many species solve TI tasks in which they learn pairs of overlapping stimulus discriminations (A+B-, B+C-, etc.) and are tested with non-adjacent novel test pairings (BD). When relations between stimuli are determined by reinforcement (A is reinforced when paired with B, B when paired with C), performance can be controlled by the associative values of individual stimuli or by logical inference. In Experiment 1 rhesus monkeys (Macaca mulatta) chose the higher ranked item on non-adjacent test trials after training on a 7-image TI task. In Experiment 2 we measured the associative values of 7 TI images and found that these values did not correlate with choice in TI tests. In Experiment 3 large experimental manipulations of the associative value of images did influence performance in some TI test pairings, but performance on other pairs was consistent with the implied order. In Experiment 4 monkeys linked two previously learned 7-item lists into one 14-item list after training with a single linking pair. Linking cannot be explained by associative values. Associative value can control choice in TI tests in at least some extreme circumstances. Implied order better explains most TI choices in monkeys, and is a more viable mechanism for TI of social dominance, which has been observed in birds and fish.

Transitive inference in pigeons: measuring the associative values of Stimuli B and D

Several reinforcement-based models have been proposed to explain transitive-like behavior in nonverbal transitive inference tasks. These models assume that the initial training required for memorizing the premises produces an ordered series of associative values (A>B>C>D>E); these values can then be used to select the "transitively correct" stimulus in a novel pair (e.g., BD). Our study experimentally tested this assumption by using resistance-to-extinction and resistance-to-reinforcement techniques to obtain empirical measures of associative strength for Stimuli B and D. We first measured the associative strengths of these stimuli after completion of initial training with overlapping pairs of colored squares (A+B-, B+C-, C+D-, and D+E-) using resistance-to-extinction and resistance-to-reinforcement procedures. Next, we used massed presentations of Pair D+E- (termed bias reversal) that ought to increase the associative value of Stimulus D, and again measured the associative strengths of the stimuli. None of our experimental measures of associative strength correlated with pigeons' behavior in the BD test or with BD performance predicted by associative models either before or after bias reversal (Wynne, 1995; Siemann and Delius, 1998). These results question validity of reinforcement-based models for explaining animals' behavior in nonverbal TI tasks.

Cognitive representation in transitive inference: a comparison of four corvid species

During operant transitive inference experiments, subjects are trained on adjacent stimulus pairs in an implicit linear hierarchy in which responses to higher ranked stimuli are rewarded. Two contrasting forms of cognitive representation are often used to explain resulting choice behavior. Associative representation is based on memory for the reward history of each stimulus. Relational representation depends on memory for the context in which stimuli have been presented. Natural history characteristics that require accurate configural memory, such as social complexity or reliance on cached food, should tend to promote greater use of relational representation. To test this hypothesis, four corvid species with contrasting natural histories were trained on the transitive inference task: pinyon jays, Gymnorhinus cyanocephalus; Clark's nutcrackers, Nucifraga columbiana; azure-winged magpies, Cyanopica cyanus; and western scrub jays, Aphelocoma californica. A simplified computer model of associative representation displayed a characteristic pattern of accuracy as a function of position in the hierarchy. Analysis of the deviation of each subject's performance from this predicted pattern yielded an index of reliance on relational representation. Regression of index scores against rankings of social complexity and caching reliance indicated that both traits were significantly and independently associated with greater use of relational representation.

Nonverbal transitive inference: Effects of task and awareness on human performance

We studied human nonverbal transitive inference in two paradigms: with choice stimuli orderable along a physical dimension and with non-orderable choice stimuli. We taught 96 participants to discriminate four overlapping pairs of choice stimuli: A+ B-, B+ C-, C+ D-, and D+ E-. Half of the participants were provided with post-choice visual feedback stimuli which were orderable by size; the other half were not provided with orderable feedback stimuli. In later testing, we presented novel choice pairs: BD, AC, AD, AE, BE, and CE. We found that transitive responding depended on task awareness for all participants. Additionally, participants given ordered feedback showed clearer task awareness and stronger transitive responding than did participants not given ordered feedback. Associative models (Wynne, 1995; Siemann and Delius, 1998) failed to predict the increase in transitive responding with increasing awareness. These results suggest that ordered and non-ordered transitive inference tasks support different patterns of performance.

Darwin's mistake: Explaining the discontinuity between human and nonhuman minds

Over the last quarter century, the dominant tendency in comparative cognitive psychology has been to emphasize the similarities between human and nonhuman minds and to downplay the differences as “one of degree and not of kind” (Darwin 1871). In the present target article, we argue that Darwin was mistaken: the profound biological continuity between human and nonhuman animals masks an equally profound discontinuity between human and nonhuman minds. To wit, there is a significant discontinuity in the degree to which human and nonhuman animals are able to approximate the higher-order, systematic, relational capabilities of a physical symbol system (PSS) (Newell 1980). We show that this symbolic-relational discontinuity pervades nearly every domain of cognition and runs much deeper than even the spectacular scaffolding provided by language or culture alone can explain. We propose a representational-level specification as to where human and nonhuman animals' abilities to approximate a PSS are similar and where they differ. We conclude by suggesting that recent symbolic-connectionist models of cognition shed new light on the mechanisms that underlie the gap between human and nonhuman minds.

Transitive inference in non-human animals: an empirical and theoretical analysis

Transitive inference has long been considered one of the hallmarks of human deductive reasoning. Recent reports of transitive-like behaviors in non-human animals have prompted a flourishing empirical and theoretical search for the mechanism(s) that may mediate this ability in non-humans. In this paper, I begin by describing the transitive inference tasks customarily used with non-human animals and then review the empirical findings. Transitive inference has been demonstrated in a wide variety of species, and the signature effects that usually accompany transitive inference in humans (the serial position effect and the symbolic distance effect) have also been found in non-humans. I then critically analyze the most prominent models of this ability in non-human animals. Some models are cognitive, proposing for instance that animals use the rules of formal logic or form mental representations of the premises to solve the task, others are based on associative mechanisms such as value transfer and reinforcement and non-reinforcement. Overall, I argue that the reinforcement-based models are in a much better empirical and theoretical position. Hence, transitive inference in non-human animals should be considered a property of reinforcement history rather than of inferential processes. I finalize by shedding some light on some promising lines of research.