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

Perspectives on Behavior Science volume 43, pages 259–283 (2020)Cite this article

Abstract

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.

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Notes

  1. Although we describe the basic model using a three-member class example, equivalence networks can occur at far greater complexity (e.g., greater class membership, multiple nodes, contextual control) and include transfers and transformations of stimulus function, all of which likely participate in much of human behavior (see Dixon, Belisle, Rehfeldt, & Root, 2018, for an overview of basic and applied research and future extensions).

  2. Here we wish to be clear about our use of this term. “Quantitative” often implies both the expression of theory as equation and a rigorous means of measuring the equation’s input and output terms. In explaining relational density theory we will show how its terms may be quantified. However, many of the studies we will mention in illustrating theory predictions were not devised with the theory in mind. In such cases we will sometimes need to resort to an ordinal description of variables, in terms of more versus less, rather than exact quantities. This reflects a limitation of the relevant studies rather than of the model.

  3. A node is an item in a network. Thus, a three-node stimulus relations network would encompass 3 stimuli.

  4. We use the term metaphor to describe the transfer of laws and rules in one context to understanding laws and rules that operate in a similar way in another context.

  5. We provide standard conceptual definitions and compare the results of prior research to predictions made by these definitions that deviate from traditional equivalence accounts. Basic research on relational density theory will need to further develop operational and computational formulas as has been done with BMT to directly test the core assumptions of the theory.

  6. In a stimulus relations network, nodal distance is the number of directly learned relations separating any two items. For instance, if experience makes A equivalent to B, and also B equivalent to C, then the nodal distance between A and B is 1. The distance between A and C is 2.

  7. Here is a simple example of reversing relations. To create the class in which A1 = B1 = C1, one might teach that A1 = B1 (but not B2), then that B1 = C1 (but not C2). After equivalence has been verified, reversal could take the form of teaching that B1 = C2 rather than C1, with the interest being in what happens to other relations (A1 = B1 and A1 = C1) that formerly depended on B1 = C1 to comprise a complete equivalence class.

  8. A possibly related effect was described by Doughty, Leake, and Stoudemire (2014), who found that derived relational testing may be a prerequisite to resurgence (i.e., resistance). Prior research has demonstrated that, in the absence of direct reinforcement, testing improves the accuracy and response speed of derived relations (e.g., Sidman, Kirk, & Willson-Morris, 1985). These effects suggest increased relational density and therefore likely increased mass.

  9. We also only condition one I–L class to eliminate relating through exclusion (i.e., if participants responses A1–I1, then they may relate A2–I2 through exclusion).

  10. A potentially useful procedure for mapping network volume and density is the Implicit Relational Assessment Procedure (IRAP; Barnes-Holmes, Hayden, Barnes-Holmes, & Stewart, 2008).

  11. A key tenet of tiered systems is that interventions are only as invasive as they need to be to produce beneficial results.

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Authors and Affiliations

  1. Missouri State University, Springfield, MO, USA

    Jordan Belisle

  2. Department of Disability and Human Development, University of Illinois at Chicago, 1640 W. Roosevelt Rd. 436 DHSP (MC 626), Chicago, IL, 60608, USA

    Mark R. Dixon

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  1. Jordan Belisle
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  2. Mark R. Dixon
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Correspondence to Mark R. Dixon.

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Belisle, J., Dixon, M.R. Relational Density Theory: Nonlinearity of Equivalence Relating Examined through Higher-Order Volumetric-Mass-Density. Perspect Behav Sci 43, 259–283 (2020). https://doi.org/10.1007/s40614-020-00248-w

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Keywords

  • classical mechanics
  • relational density theory
  • relational frame theory
  • stimulus equivalence