The concept of symmetry in behavior has been extended from its original focus on bilateral symmetry of the human body to the role of symmetry as one of the defining characteristics of equivalence relations. Without symmetry and equivalence relations, what people refer to as classification, symbolism, reference, representation, and semantic meaning would play considerably less significant roles in verbal behavior and language.

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Three theories have been proposed in behavior analysis to explain the establishment of stimulus equivalence. Sidman's (1994) equivalence relation theory suggests that stimulus equivalence is a fundamental behavioral function caused by reinforcement contingencies, and asserts that learning is unnecessary for its establishment. In contrast, the relational frame theory (RFT) suggests that stimulus equivalence results from previous learning regarding many different stimulus-relationships. On the other hand, the naming theory focuses on the naming process, or the circular relationship between the behaviors of the speaker-listener. The latter two theories hold that verbal learning is necessary for the formation of stimulus equivalence. Moreover, naming theory suggests that equivalence relations are formed by verbal responses, whereas the other two theories suggest that naming is the same behavioral process as equivalence. In conclusion it is suggested that analysis of stimulus function is crucial to understand cognition and language.

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In this paper, I briefly summarize the research history on the (non-) emergence of symmetry in the chimpanzees of the Primate Research Institute, Kyoto University. The chimpanzee Ai, who had learned the visual artificial symbols (lexigrams), did not exhibited the spontaneous emergence of symmetry between name and objects, but showed gradual improvement during the repeated exposure of training-testing cycles. This repeated exposure effect on the emergence of symmetry was also observed in the other individual who were not “language-trained”. This chimpanzee also exhibited the control by exclusion, which is considered as another type of illogical biases in humans. Chimpanzees also showed significant effect of differential outcome and differential responding on symmetry. Conclusion so far is that chimpanzees show no emergence of symmetry immediately after the training of conditional discriminations. Repeated exposure of training-testing contexts, however, has critical effect on the emergence of symmetry. For the future direction, it is suggested to promote studying the symmetry bias during the causal reasoning not using traditional conditional discrimination paradigm from the comparative-cognitive perspective.

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Dolphins are known to exhibit highly developed social interactions, and numerous high advanced social behaviors have been observed in their school. We conducted a variety of tasks to understand the cognitive abilities of beluga (Delphinapterus leucas). Symmetry, a cognitive ability that is only present in a few nonhuman animals, was tested in a male beluga ten years ago (1997). At that time, however, it was found that the subject performed poorly. Here we report the results of our observations which set about to determine whether cognitive mechanisms, such as symmetry, could be altered or developed over a relatively long period of time (i.e. 10 years). We used the same beluga that was used for the symmetry tests conducted 10 years previously. Using the same procedures employed in the first test, the subject was observed to exhibit symmetry. Since the subject has been engaged in a variety of cognitive tasks other than tests of symmetry over the past 10 years, it is proposed that these experiences have positively influenced the development of symmetry in this animal.

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Researchers studying symmetry, one of the requirements for establishing stimulus equivalence, have contrasted inferences made by human and nonhuman animals and suggested that inference in each animal species is determined by several biological factors developed in the course of the evolution of a given species. This paper reviews the relevant experimental studies with human and nonhuman animals, including studies of young children, individuals with developmental disabilities, and nonhuman mammals. This work indicates that developmental, ethological, and behavioral factors are closely related to produce symmetry. In searching for the neural factors of symmetry, evidence from fMRI studies suggests that brain activity associated with equivalence relationships occurs in the processing of stimuli with or without temporal order. Thus, further research on the processing of temporal-spatial factors of stimuli is needed in both human and nonhuman animals. A detailed analysis of human subjects failing to establish equivalence relationships, and of nonhuman animals performing prerequisites for symmetry, such as identity matching and matching by exclusion, is crucial for understanding the biological origins of symmetry inferences.

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It has been demonstrated that there are many similarities between Pavlovian conditioning in nonhuman animals and causal judgment by humans, such as conditioned inhibition, overshadowing, and blocking. However, there was a notable difference in empirical studies between animal Pavlovian conditioning and human causal judgment: lack of retrospective inference (i.e., backward blocking) in animals. Although human participants showed symmetrical results for forward and backward blocking procedure in causal judgment, researchers failed to obtain backward blocking in animal conditioning. In the case of forward blocking, a cue is first paired with an unconditioned stimulus (US) (e.g., A+), and the first cue is then presented together with a target cue and the US (e.g., AX+). In the case of backward blocking, the compound cue is learned first (AX+), and then the competing cue alone is paired with the US (A+). In subsequent tests, human participants inferred in both cases that X is not a cause of the outcome, whereas the response of animals to X alone was “blocked” only in the forward blocking procedure but not in the backward one. In this article, we review the existence studies on retrospective inference in humans and animals including our ongoing primate study and explore a possible role of retrieval deficits in memory for retrospective inference in animals.

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The ability to pass tests of stimulus equivalence seems to mark an important distinction between animals and humans that is tied to language. Most other animals are unable to reliably pass equivalence tests. Even linguistically trained chimps seem unable to pass them (Dugdale & Lowe, 1990). Moreover, pre-linguistic children show similar poor performance. Sidman (1990) argues that an innate logic (Fodor, 1975) would confuse explanandum with explanans, i.e., logical ability needs to be explained by more primitive behaviour. We argue that abductive reasoning ability is more primitive in that it is required to learn basic stimulus-stimulus relations. Moreover, we propose that extending this ability beyond the temporal limitations of our neural equipment requires the ability to sustain a representation in working memory and this may be facilitated by associating it with an endogenous rehearsable response, i.e., a speech sound. In sum, extending the temporal range over which associations can be learned using associated sound may tie together the origins of reasoning, language and working memory.

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Many fallacies and biases in human reasoning and judgment have been reported individually, but their relationships have rarely been argued, and we are still far from a unified psychological theory of thinking. In this paper, equiprobability is proposed as a key concept in human thinking from a Bayesian probabilistic perspective. The importance of the equiprobability assumption, together with the rarity assumption and a tendency to seek information, is suggested from the results of our probabilistic approaches to various tasks. These tasks include deduction, induction, and probability judgment, including the Wason selection task, covariation assessment, hypothesis testing, and base-rate neglect. People seem to have a general tendency to assume the equiprobability of any two target events they encounter. Using ideas obtained from studies of inference in animals and in people with schizophrenia, the adaptive implications of symmetrical inference, based on its relationships with the phylogenetic origins of human creativity, language, and social intelligence, are discussed.

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Symmetry bias is sometimes regarded as a culprit that results in fallacies and spoils our logically correct reasoning. We believe, however, that this bias is also indispensable if we are to obtain unfamiliar notions, to think creatively, and to infer heuristically. We devised an algorithm which can overcome the “exploration-exploitation dilemma” that is involved in the decision-making process under conditions of uncertainty, via a computer simulation based on the “2-armed Bandit Problem.” As a result, we confirmed that the agent-model, which contains both kinds of symmetry biases, displayed very flexible behavior, and that it achieved drastically higher scores than the other mechanical agents. In this paper, by drawing upon the theory of ‘Bi-logic’ as developed by Matte Blanco, we discuss why human-beings require this kind of illogicality, and how fundamental it is for human [un]consciousness.

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Causal induction about contingency information has been the subject of debates, between the power PC theory, associative learning theory, and symmetry bias theory. Whereas most researchers in the subject area agree that cognitive bias is normative induction process overestimating particular cause-effect associations, the question remains how the cognitive bias is originated in humans' behaviors. This article offers a dynamical logic called ad-hoc logic, based on a lattice (topped intersection structure), that is continuously removing and/or adding its own elements. The ad-hoc logic implements the negotiation process between the system of representations (type) and that of objects (token). The asymmetry between types and tokens embedded in the ad-hoc logic can paradoxically lead to symmetry bias. The model is consistent with experimental results of causal judgments in literature.

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It is well known that the symmetry bias much accelerates the process of vocabulary learning, especially in infants' first language acquisition where they easily tend to connect objects with their names. However, the grammar learning is another important aspect of language acquisition. In this study, we contended that the symmetry bias also would help to learn grammar rules. We employed Kirby's model (Iterated Learning Model; ILM) in which the parental speakers uttered sentences with their semantic representaions and children guessed the background grammar in their minds; in turn, children became new parents and generated sentences in the following generation. We revised this model to include utterances without semantics. We have shown that children could abduce the meanings from utterances by the symmetry bias, and that they acquired the same language with smaller number of learning data by computer simulation.

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In this commentary paper, we discuss what symmetrical and bidirectional reasoning might have brought to humans by overviewing a collection of papers contributed to the special feature “Symmetry” in this volume. Several authors noted that bidirectional reasoning is deeply related to the ability to make abductive inference, which in turn allows quick and efficient reasoning and decision making based on heuristics. We point out that quick and efficient inference using heuristics is the very characteristics of young children's early word and concept learning as well, and speculate that well known biases children show in early word and concept learning could be explained as a consequence of abductions children have quickly formed through short exposure to language. Thinking this way, disposition to make bidirectional inference could potentially serve as a crucial building block (i.e., the prerequisite) for the competence of language in humans rather than the other way around. All in all, the papers contributed to the special feature forcefully suggest that thinking based on heuristics rather than logic is hallmark of human intelligence rather than limitation, and the disposition to draw bidirectional inference plays a key role there.

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This commentary gave some additional findings and implications for “symmetrical bias (or bidirectional relation)” from a viewpoint of Contextual Behavioral Science, in particular, Relational Frame Theory and Acceptance and Commitment Therapy. The given findings were related with a) the transformation of stimulus function through bidirectional relation in persons with specific phobia or mental disorder, b) the emergence or non-emergence of bidirectional relation influenced by baseline-training reversals or protocols in matching-to-sample procedure, and c) the emergence or non-emergence of bidirectional relation in infants or nonhuman subjects. Furthermore, the given implications were related with d) necessity of balancing between abduction and induction, particularly identifying and cumulating the manipulable variables inductively, e) prevention of confusing explanation with cause through symmetrical biases, and f) clarification of own ”purpose and value”, in pursuing symmetry bias or bidirectional relation as one of most fundamental processes in human cognition.

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The substance of the mirror-reversal problem can be thoroughly understood by a completely logical analysis based on the physical knowledge about mirror images without special mental⁄psychological idea, except to see the observer's own mirror image as a real object.

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The difference between Kokame and Tabata hypotheses on the mirror problem comes from the rejection of the notion of the mirror image's intrinsic frame of reference by the former. However, this rejection has no solid reason.

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Objection to criticism by Tabata about the consideration of true meanings of the mirror-reversal by Kokame is discussed. A fatal error in his definition of the inherent coordinate-system of human mirror-image is analyzed in detail and demonstrated.

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[in Japanese]

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Objection to criticism by Takano about the consideration of true meanings of mirror reversal by Kokame is discussed. A fatal error and general logical⁄cognitive mistakes in his argument are demonstrated.

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When one uses intrinsic frames of reference separately for an asymmetric object and its mirror image, one perceives the mirror image as left-right reversed because of such a nature of the left-right axis that it is determined depending on the top-bottom and front-back axes. When one perceives the mirror image as left-right nonreversed, on the other hand, one is applying a common frame of reference to the object and its mirror image, obtaining the simple result of geometric optics.

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Fatal error of the idea of Tabata is to separate the mirror reversal problem into two categories, namely, the left-right positional reversal of mirror images which is optically non-existing fact, and the left-right non-reversal which is the true optical fact, and then prove individually two cases are both true as physical facts by misuse of inherent coordinate systems.

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All of Kokame's arguments against Tabata hypothesis are rejected as invalid. Instead, those arguments have clearly revealed that Kokame's hypothesis has no reason of its existence.

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Tabata (2008) modified Tabata and Okuda's (2000) account of mirror reversal by importing three explanatory principles from Takano's (1998) multi-process theory. However, it is found that the modified account is still unable to explain many of Takano and Tanaka's (2007) experimental findings, which can be readily explained by the multi-process theory.

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All of Takano's arguments against Tabata hypothesis are rejected as invalid. Thus the validity and solidity of Tabata hypothesis have been proved.

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This paper summarizes the explanation of mirror reversal based on the multi-process theory proposed by Takano (1997, 1998). It also presents some empirical evidence to prove that the left-right mirror reversal of a viewer' own and that of an alphanumeric character are produced by different underlying principles, respectively.

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The common misapprehension that the left-right positional mirror reversal exists truly is being believed by Takano who has proposed the Multi-Process Hypothesis. His logic to prove real existence of the mirror reversal inevitably contains logical mistakes. The specific defects of the hypothesis are pointed out by simple logical analysis.

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Kokame (2008b) has criticized Takano's (1998) assumption of viewpoint transformation in the mirror reversal of a viewer. This paper shows its necessity as well as invalidity of Kokame's alternative method of judging left and right.

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Takano's hypothesis treats the psychological processes of mirror image perception; and Tabata's, its physical basis. Properly speaking, these two approaches should be united. To make the unification possible, however, the physical conception on which Takano's hypothesis is constructed should be rectified.

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Tabata (2008b) has criticized Takano and Tanaka's (2008) account of mirror reversal in that it is based on “incomplete comprehension of physical principles.” However, Tabata's comprehension of physical principles is invalid in that it implicitly includes many cognitive processes as well.

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