Specific types of relational responding, termed relational frames, are defined in terms of the three properties of mutual and combinatorial entailment, and the transformation of functions. Relational frames are arbitrarily applicable, but are typically not necessarily arbitrarily applied in the natural language context.

Mutual entailment refers to the derived bidirectionality of some stimulus relations, and as such it is a generic term for the concept of "symmetry" in stimulus equivalence. "Mutual entailment" applies if stimulus A is related to another stimulus B in a specific context, and as a result a relation between B and A is entailed in that context. 

Combinatorial entailment refers to instances in which two or more relations that have acquired the property of mutual entailment mutually combine. Combinatorial entailment is the generic term for what is called "transitivity" and "equivalence" in stimulus equivalence. Combinatorial entailment applies when, in a given context, A is related to B and B is related to C, and then in that context a relation is entailed between A and C and another between C and A. For example, if A is bigger than B, and B is bigger than C, then a bigger-than relation is entailed between A and C, and a smaller-than relation is entailed between C and A. 

A transformation of stimulus functions applies when functions of one event in a relational network is altered based on the functions of another event in the network and the derived relation between them. Mutual and combinatorial entailment are regulated by contextual cues (C rel). The transformation of stimulus functions are regulated by additional contextual cues (C func).

The development of relational responding can be organized into a rough list that gradually becomes more and more complex. We are not presenting this list as a set of stages or steps, and we would expect them to be sequenced only in broad terms and even then only if the training history is typical. Nevertheless, this list gives a sense of the complexity that emerges from the small set of core concepts in Relational Frame Theory.

• Contextually controlled mutual entailment in equivalence
• Contextually controlled combinatorial entailment in equivalence
• Contextually controlled transfer of stimulus functions through equivalence relations
• Integration of these response components into a functional response class: a frame of coordination
• Simple examples of verbal understanding
• Contextually controlled mutual entailment in additional types of stimulus relations
• Contextually controlled combinatorial entailment in additional types of stimulus relations
• Contextually controlled transformation of stimulus functions in additional types of stimulus relations
• Integration of these into additional relational frames
• Simple examples of genuinely verbal governance of behavior by others
• Conditional contextual control over the participation of given elements in relational frames
• The development of relational networks
• More complex examples of verbal understanding
• Verbal governance of the behavior of others (e.g., verbal mands and tacts)
• Transformation of stimulus functions across relational networks
• Increasing number and complexity of relational frames
• Increasing acquisition of specific participants in specific relational frames (e.g., vocabulary)
• Complex interactions between relations (training in one influences development of another)
• Integration of related types of relational frames into families of relational responses
• Elaborated and increasingly subtle contextual control over relational responding (e.g., syntax; number of relational terms)
• Elaborated and increasingly subtle contextual control over transformation of stimulus functions (e.g., number and specificity of functional terms)
• Nonarbitrary properties serve as a relational context for arbitrarily applicable relational responses
• Increasingly complex relational networks
• With acquisition of equivalence, time or causality, and evaluation, the development of relational sentences that function fully as rules
• Relating relational networks
• Transformation of stimulus functions based on the relating of relational networks
• Relating relational networks under the control of nonarbitrary properties of the environment
• More complex examples of rule understanding and rule-governance, particularly pliance and tracking
• Regulation of the behavior of the listener through the establishment of relational networks in the listener
• With the acquisition of hierarchical class membership, use of relational networks to abstract nonarbitrary properties and to have these properties participate in relational frames
• Abstracting properties of the nonarbitrary environment based on relational networks and the relating of relational networks
• With the acquisition of temporal, contingency, and causal relational frames, increased insensitivity to temporal delays
• Development of deictic relational frames
• Development of perspective-taking and sense of self
• Construction of the verbal other
• Construction of the conceptualized group
• Contextual control of relational responding by the nonarbitrary and arbitrary properties of the listener
• Further development of rule-following, particularly augmenting
• Regulation of the behavior of the listener by orienting the listener to abstracted features of the environment
• Acquisition of increasingly abstract verbal consequences
• Self-rule generation and self rule-following
• Pragmatic verbal analysis and increasingly complex forms of problem solving and reasoning
• Increasing dominance of the verbal functions of the environment

Relational responding involves generalized responding in accordance with a pattern of relations between stimuli, rather than responding to a stimulus on the basis of one or a limited number of associations. RFT proposes that relational framing, or relating, is generalized operant behavior.

Like all operants, relational framing is influenced by and can only be understood within its current and historical context. Relational framing also demonstrates the primary characteristics of all operant behavior:

• Acquisition and strengthening over time through a history of reinforcement/multiple exemplar training
• Flexibility/changes in response to changes in the environment
• Influence by antecedent stimulus control
• Influence by consequential stimulus control

Like any other operant, relational framing is a skill that can be fragile (e.g., less widely generalized, with a slow rate of responding) or stronger (e.g. more widely generalized, fluent). Thus, practice in relational framing would be expected to strengthen the operant and result in more fluent responding in any context in which deriving relations is relevant—that is, almost any language-based task. Research on relational training has suggested that not only can multiple exemplar training result in the acquisition of framing repertoires if not already present, but that strengthening existing relational repertoires can result in significant increases in standardized cognitive and academic measures across a range of populations. Such work supports the core RFT thesis that relational framing as an operant is central to human language in all its potential generativity and complexity.

For further reading on relating as an operant, see:

Hayes, S. C., Law, S., Assemi, K., Falletta-Cowden, N., Shamblin, M., Burleigh, K., Olla, R., Forman, M., & Smith, P. (2021). Relating is an Operant: A Fly Over of 35 Years of RFT Research. Perspectivas em Análise do Comportamento. https://doi.org/10.18761/pac.2021.v12.rft.02

Hughes, S., & Barnes‐Holmes, D. (2015). Relational Frame Theory: The Basic Account. In R. D. Zettle, S. C. Hayes, D. Barnes-Holmes, & A. Biglan (Eds.), The Wiley handbook of contextual behavioral science (pp. 129-178). John Wiley & Sons.