Stimulus equivalence and transitive associations: A methodological analysis

What, if anything, can be considered an amodal sensory dimension?

The term 'amodal' is a key topic in several different research fields across experimental psychology and cognitive neuroscience, including in the areas of developmental and perception science. However, despite being regularly used in the literature, the term means something different to the researchers working in the different contexts. Many developmental scientists conceive of the term as referring to those perceptual qualities, such as, for example, the size and shape of an object, that can be picked up by multiple senses (e.g., vision and touch potentially providing information relevant to the same physical stimulus/property). However, the amodal label is also widely used in the case of those qualities that are not directly sensory, such as, for example, numerosity, rhythm, synchrony, etc. Cognitive neuroscientists, by contrast, tend to use the term amodal to refer to those central cognitive processes and brain areas that do not appear to be preferentially responsive to a particular sensory modality or to those symbolic or formal representations that essentially lack any modality and that are assumed to play a role in the higher processing of sensory information. Finally, perception scientists sometimes refer to the phenomenon of 'amodal completion', referring to the spontaneous completion of perceptual information that is missing when occluded objects are presented to observers. In this paper, we review the various different ways in which the term 'amodal' has been used in the literature and the evidence supporting the various uses of the term. Morever, we highlight some of the various properties that have been suggested to be 'amodal' over the years. Then, we try to address some of the questions that arise from the reviewed evidence, such as: Do different uses of the 'term' refer to different domains, for example, sensory information, perceptual processes, or perceptual representations? Are there any commonalities among the different uses of the term? To what extent is research on cross-modal associations (or correspondences) related to, or can shed light on, amodality? And how is the notion of amodal related to multisensory integration? Based on the reviewed evidence, it is argued that there is, as yet, no convincing empirical evidence to support the claim that amodal sensory qualities exist. We thus suggest that use of the term amodal would be more meaningful with respect to abstract cognition rather than necessarily sensory perception, the latter being more adequately explained/understood in terms of highly redundant cross-modal correspondences.

Crossmodal associations between visual textures and temperature concepts

Visual textures are critical in how individuals form sensory expectations about objects, which include somatosensory properties such as temperature. This study aimed to uncover crossmodal associations between visual textures and temperature concepts. In Experiment 1 (N = 193), we evaluated crossmodal associations between 43 visual texture categories and different temperature concepts (via temperature words such as cold and hot) using an explicit forced-choice test. The results revealed associations between striped, cracked, matted, and waffled visual textures and high temperatures and between crystalline and flecked visual textures and low temperatures. In Experiment 2 (N = 247), we conducted six implicit association tests (IATs) pairing the two visual textures most strongly associated with low (crystalline and flecked) and high (striped and cracked) temperatures with the words cold and hot as per the results of Experiment 1. When pairing the crystalline and striped visual textures, the results revealed that crystalline was matched to the word cold, and striped was matched to the word hot. However, some associations found in the explicit test were not found in the IATs. In Experiment 3 (N = 124), we investigated how mappings between visual textures and concrete entities may influence crossmodal associations with temperature and these visual textures. Altogether, we found a range of association strengths and automaticity levels. Importantly, we found evidence of relative effects. Furthermore, some of these crossmodal associations are partly influenced by indirect mappings to concrete entities.

Emergent Relations between Discriminative Stimuli, Responses, and Consequences in Intraverbals

We explored the emergence of relations between stimuli learned as discriminative, responses, and consequences with intraverbals. In Experiment 1, five 9- and 10-year-old children learned intraverbals that related a country (A) with a city (B)—e.g., “Name a city of Switzerland”; “Davos”—and that country with a predator animal (C). Correct responses were followed by saying the name of a feature of the city (T) or saying an animal preyed by the predator (U), respectively. The emergence of BC and CB intraverbals that relate the cities and the predators and that of intraverbals that relate the specific consequences to the cities (T-B and U-B) and to the prey animals (T-C and U-C) was probed with no differential consequences. All five children demonstrated the emergence of BC, CB, U-B, and U-C and four children also demonstrated the emergence of T-B and T-C. In Experiment 2, a simpler procedure that controlled a possible extraneous factor, was used with seven 7- and 8-year old children and they also demonstrated emergence. Thus, the emergence of verbal relations with elements taught as discriminative stimuli, responses, and consequences was demonstrated.

The effect of dimensional reinforcement prediction on discrimination of compound visual stimuli by pigeons

We trained eight pigeons (Columba livia) on a stagewise go/no-go visual discrimination task. A total of 16 visual stimuli were created from all possible combinations of four binary dimensions: brightness (dark/bright), size (large/small), line orientation (vertical/horizontal), and shape (circle/square). In the first stage, we presented S + and four S- stimuli: sharing one (brightness), two (brightness and orientation), three (brightness, orientation, and size), or no dimensional values with S + . In the second stage, all 16 stimuli were presented. In the first stage, stimulus discrimination was controlled by the number of dimensional disparities between non-rewarded stimuli and a rewarded one rather than by stimulus dimensional salience, whereas at the beginning of the second stage, pigeon behaviour was controlled mainly by dimensional reinforcement expectancy learned in the first stage. At the beginning of the second stage, pigeons correctly rejected 6-8 of 11 new added S- stimuli. A significant inverse correlation between the number of S- stimuli sharing dimension values with S + in the first stage and the dimensional discrimination ratios at the beginning of the second stage was found.

Mediated Generalization and Stimulus Equivalence

From the 1930s to the 1970s a large number of experimental studies on mediated generalization were published, and this research tradition provided an important context for early research on stimulus equivalence. Mediated generalization and stimulus equivalence have several characteristics in common, notably that both traditions seek to experimentally investigate derived responding among arbitrarily related stimuli in human participants. Although studies of stimulus equivalence are currently being regularly published, few studies investigate mediated generalization in humans today, and the research tradition is mainly of historical interest. The current article will give an account of the origin, the development, and the demise of research on mediated generalization, including a presentation of publication trends, experimental methodology, and the conceptual context research on mediated generalization took place within. Finally, some thoughts on the demise of mediated generalization and its relevance for modern research on stimulus equivalence and other types of derived responding are presented, including reflections on the observability of explanatory variables and the use of inferential statistics.

A descriptive analysis of baseline and equivalence-class performances under many-to-one and one-to-many structures

The purpose of the present experiment was to describe responding as a function of One-to-Many (OTM) and Many-to-One (MTO) training structures and identify baseline performances correlated with the accuracy level in tests for equivalence class formation. Participants were 42 adults assigned to either the MTO or the OTM groups, trained on 24 baseline relations, and assessed on the emergence of three 9-member equivalence classes. Participants in the MTO group presented similar frequencies of responses to each of the comparisons throughout baseline training. Also, the number of trials required to meet the baseline mastery criterion was negatively correlated with test accuracy. Participants in the OTM group presented more variable frequencies of responses to each of the comparisons (participants tended to select some of the comparisons less often than others at the beginning of the training). In addition, the number of reinforced responses to the node presented as a sample during training was positively correlated with the number of correct responses during testing for the OTM group. The experiment contributed to an in-depth stimulus control analysis of baseline and test performances, and its results have implications for understanding potential sources of variability between the training structures.

Effects of preliminary class membership on subsequent stimulus equivalence class formation

The present study examined the effects of including stimuli previously trained as members of functional classes or equivalence classes on subsequent equivalence class formation, and isolated the effects of preliminary training from those of the acquired function stimuli. Fifty-six adults were assigned to 1 of 5 conditions. The control group (CONT) received no preliminary training prior to the terminal phase. Participants in the other 4 groups learned two 3-member functional classes and two 3-member equivalence classes during the preliminary phase. The terminal equivalence phase trained two 5-member classes (A → B → C → D → E) comprising abstract forms; the C stimuli in the terminal phase were (a) from the preliminary functional classes for 1 group (ACQ-F), (b) from the preliminary equivalence classes for the second experimental group (ACQ-E), (c) pictures of everyday objects for the picture control group (PIC), and (d) novel, unfamiliar stimuli for the preliminary training control group (PRE-CONT). Class formation yields were 100% in the PIC condition and 11% in the CONT condition; however, low yields in the PRE-CONT, ACQ-F, and ACQ-E conditions were unexpected, suggesting that procedural variables in preliminary training account for more of the subsequent effects on class formation than the stimulus control properties of the acquired function stimuli.

Relational Density Theory: Nonlinearity of Equivalence Relating Examined through Higher-Order Volumetric-Mass-Density

We propose relational density theory, as an integration of stimulus equivalence and behavioral momentum theory, to predict the nonlinearity of equivalence responding of verbal humans. Consistent with Newtonian classical mechanics, the theory posits that equivalence networks will demonstrate the higher order properties of density, volume, and mass. That is, networks containing more relations (volume) that are stronger (density) will be more resistant to change (i.e., contain greater mass; mass = volume * density). Data from several equivalence experiments that are not easily interpreted through existing accounts are described in terms of the theory, generating predictable results in most cases. In addition, we put forward the higher-order properties of relational acceleration and gravity, which follow directly from the theory and may inspire future researchers to evaluate the seemingly self-organizing nature of human cognition. Finally, we conclude by describing avenues for real-world translation, considering past research interpreted through relational density theory, and call for basic experimental research to validate and extend core theoretical assumptions.

Sidman Goes to College: A Meta-Analysis of Equivalence-Based Instruction in Higher Education

Equivalence-based instruction (EBI) is a pedagogy based on the principles of stimulus equivalence for teaching academically relevant concepts. This self-paced and mastery-based methodology meets many of the instructional design standards suggested by Skinner (1968), adds generative learning by programming for derived stimulus-stimulus relations, and can be particularly useful in the context of a college course in which students must learn numerous concepts. In this article, we provide the first meta-analysis of EBI in higher education. The authors conducted a systematic literature search that identified 31 applied, college-level EBI experiments across 28 articles. Separate meta-analyses were conducted for single-subject and group design studies. Results showed that EBI is more effective than no instruction and an active control and that studies comparing EBI variants show differences between training variants. Future research should increase internal, external, and statistical conclusion validity to promote the mainstream use of EBI in classrooms.

Effects of orientation and differential reinforcement II: transitivity and transfer across five-member sets

A recent report by Amd et al. (2017) demonstrated that orienting towards successively presented stimulus-stimulus pairs yielded significantly more transitive relations then when those same pairs were differentially reinforced following training for three, 3-member stimulus sets. We build on that work in four important ways. First, transitivity yields produced by Pavlovian and instrumental procedures were compared following training for three 5-member sets (A1-B1-C1-D1-E1, A2-B2-C2-D2-E2, A3-B3-C3-D3-E3), where the 'A' stimuli were emotional faces and all remaining stimuli were nonsense words. Second, our instrumental task here required two orienting/observing responses per trial. Third, we compared differences in multi-nodal transfer following Pavlovian and instrumental relational learning procedures. Finally, we tested whether functioning as 'end terms' in a relational series can mitigate transfer following instrumental conditioning. Transitivity, as measured by sorting tests, was significantly more pronounced following Pavlovian training. Transfer, assessed before and after relational training with two visual analog scales corresponding to valence and arousal dimensions, appeared marginally more robust observed for participants exposed to the Pavlovian condition. Transfer magnitude was positively related with demonstrations of transitivity, regardless of type of conditioning.

Establishing Derived Equivalence Relations of Basic Geography Skills in Children with Autism

The present study evaluated the efficacy of a stimulus-equivalence training procedure in teaching basic geography skills to two children with autism. The procedures were taken directly from a standardized training curriculum based in stimulus equivalence theory called Promoting the Emergence of Advanced Knowledge Equivalence Module (PEAK-E). Results suggest that the procedures were efficacious in directly training several geographical relations, as well as promoting the derivation of several untrained relations for three countries and their corresponding continents. In addition, responding generalized from selecting countries on a tabletop paper map to selecting countries on an interactive touchscreen map.

Effects of orientation and differential reinforcement on transitive stimulus control

The emergence of transitive relations between stimuli that had never appeared together is a key process underlying concept formation. An unresolved theoretical issue with respect to transitive relations has been to determine whether differential reinforcement of stimulus-stimulus (S-S) relations though matching-to-sample, or contiguous S-S correlations/pairings, is more critical for producing transitivity. The current study inquired whether simple environmental S-S pairings, versus differential reinforcement of S-S relations, versus environmental S-S pairings with an orientation requirement, produced the greatest instances of transitivity. 12 groups of participants were parsed into one of four procedures (matching-to-sample, stimulus-paring, stimulus-pairing-w/response, stimulus-pairing-w/orientation) along one of three training structures (linear, many-to-one, one-to-many). All participants underwent a fixed number of training trials for establishing three, three-member stimulus sets (A1B1C1, A2B2C2, A3B3C3), followed by a single sorting test for AC transitivity. Our results demonstrate orienting towards environmental S-S pairings yield the greatest degree of transitivity. The effectivity of pairing procedures for establishing transitive relations, particularly when compared to matching-to-sample, can inform the development of educational interventions for individuals for whom the latter procedure (involving differential reinforcement) is ineffective.

Transitive and anti-transitive emergent relations in pigeons: support for a theory of stimulus-class formation

Stimulus class formation is inferred when conditional discrimination training yields new (emergent) conditional relations between the training stimuli. The present experiments demonstrated two such relations in pigeons after successive matching-to-sample training. Experiment 1 showed that transitivity (AC matching) emerged after training on AB and BC arbitrary matching plus BB identity matching: pigeons responded relatively more to the comparisons on AC test trials in which both the A samples and C comparisons were elements of reinforced arbitrary baseline relations involving the same nominal B stimulus. Experiment 2 showed the opposite effect ("anti-transitivity") after training on the same arbitrary relations but with BB oddity instead: pigeons responded relatively more to the comparisons on AC test trials in which the A sample was an element of a reinforced baseline relation and the C comparison was an element of a non-reinforced baseline relation, or vice versa. Experiment 2 also showed that AB and BC training alone generally does not yield an emergent effect. These findings extend the range of emergent phenomena observed in non-human animals and are consistent with predictions from Urcuioli's (2008) theory of pigeons' stimulus class formation. This article is part of a Special Issue entitled: Tribute to Tom Zentall.