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Technical Notation as a Tool for Basic Research in Relational Frame Theory

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A core overarching aim of Relational Frame Theory (RFT) research on language and cognition is the prediction and influence of human behavior with precision, scope, and depth. However, the conceptualization and delineation of empirical investigations of higher-order language and cognition from a relational framing theoretical standpoint is a challenging task that requires a high degree of abstract reasoning and creativity. To that end, we propose using symbolic notation as seen in early RFT experimental literature as a possible functional-analytical tool to aid in the articulation of hypotheses and design of such experiments. In this article, we provide examples of aspects of cognition previously identified in RFT literature and how they can be articulated rather more concisely using technical notation than in-text illustration. We then provide a brief demonstration of the utility of notation by offering examples of several novel experiments and hypotheses in notation format. In two tables, we provide a “key” for understanding the technical notation written herein, which other basic-science researchers may decide to draw on in future. To conclude, this article is intended to be a useful resource to those who wish to carry out basic RFT research on complex language and cognition with greater technical clarity, precision, and broad scope.
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RFT NOTATION FOR BASIC RESEARCH 2
Technical Notation as a Tool for Basic Research in Relational Frame Theory
Shane McLoughlin2
Ian Tyndall1
Teresa Mulhern2
Sam Ashcroft2
1 Department of Psychology, University of Chichester, UK
2 Department of Psychology, University of Chester, UK
Corresponding Author: Dr. Ian Tyndall, Department of Psychology, University of Chichester,
West Sussex, PO196PE, UK. Email: I.Tyndall@chi.ac.uk. Ph: 0044-1243-816421
RFT NOTATION FOR BASIC RESEARCH 3
Abstract
A core overarching aim of Relational Frame Theory (RFT) research on language and cognition is
the prediction and influence of human behavior with precision, scope, and depth. However, the
conceptualization and delineation of empirical investigations of higher-order language and
cognition from a relational framing theoretical standpoint is a challenging task that requires a
high degree of abstract reasoning and creativity. To that end, we propose using symbolic notation
as seen in early RFT experimental literature as a possible functional-analytical tool to aid in the
articulation of hypotheses and design of such experiments. In this article, we provide examples
of aspects of cognition previously identified in RFT literature and how they can be articulated
rather more concisely using technical notation than in-text illustration. We then provide a brief
demonstration of the utility of notation by offering examples of several novel experiments and
hypotheses in notation format. In two tables, we provide a “key” for understanding the technical
notation written herein, which other basic-science researchers may decide to draw on in future.
To conclude, this article is intended to be a useful resource to those who wish to carry out basic
RFT research on complex language and cognition with greater technical clarity, precision, and
broad scope.
Keywords: relational frame theory, basic research, notation, experimentation, precision, future
research
RFT NOTATION FOR BASIC RESEARCH 4
Technical Notation as a Tool for Basic Research in Relational Frame Theory
We are at an interesting juncture in our capacity to provide parsimonious yet fruitful
behavior-analytic accounts of verbal or symbolic behavior. In the present article, we highlight a
somewhat neglected but highly pragmatic Relational Frame Theory (RFT; Hayes, Barnes-
Holmes, & Roche, 2001) technical notation that may help interested researchers in the field to
(1) formulate precise research questions and empirical designs, and (2) to avoid middle-level
terms while conducting basic research. We then develop this notation to allow researchers to use
it to (1) formulate testable hypotheses with precision, and (2) to design studies of complex
cognition that are logical extensions of existing theory, but are difficult to clearly articulate in
colloquial terms. Finally, we offer several concise novel hypotheses using this notation. This
article is aimed at experimental researchers who program and run basic-science experiments
rather than applied researchers concerned with testing “middle-level” applications of RFT. We
anticipate that the use of this notation could increase the efficiency of scientific research
communication and decrease the encroachment of middle-level terms within RFT laboratories
when working out fundamental principles upon which therapies are based.
Language generativity and symbolism remain difficult challenges for behavior analysts to
satisfactorily explain with traditional accounts (see Malott, 2003; Stewart, McElwee, & Ming,
2013). However, stimulus equivalence (SE; Sidman, 1971, 1994) and derived relational
responding (e.g., RFT) have significantly contributed to our ability to understand, explain,
predict, and influence higher-order cognition (see Dymond & Roche, 2013 for a book-length
review). Within RFT, derived relational responding has occasionally been termed arbitrarily
applicable relational responding (AARR). An apparent link between AARR and language (e.g.,
Devany, Hayes & Nelson, 1986; Dickins et al., 2001) provides evidence that symmetrical,
RFT NOTATION FOR BASIC RESEARCH 5
reflexive and transitive responding are features of language underlying its generativity and
complexity. RFT has thereby allowed researchers to concisely define some of the most complex
processes by which organisms adapt to their environments, thanks to the operational precision of
behavior-analytic research.
The Need for More Basic Research
To date, both basic and applied AARR research has advanced our understanding of
language and cognition in numerous ways. However, despite the acknowledged link between
AARR and phenomena of practical interest (see Barnes-Holmes, Hussey, McEnteggart, Barnes-
Holmes, & Foody, 2016; Cassidy, Roche, Colbert, Stewart, & Grey, 2016), it is increasingly
apparent that our understanding of AARR is far from complete and it is necessary to elucidate
the fundamental features and utility of AARR further (see Dymond, Roche, & Bennett, 2013).
The need for further research is particularly acute for proponents of Acceptance and
Commitment Therapy (ACT; Hayes, Strosahl, & Wilson, 1999) who regularly refer to the critical
link between RFT and ACT (see Barnes-Holmes et al., 2016). It is proposed that RFT accounts
for a number of core techniques or strategies employed by ACT therapists (e.g., heavy reliance
on the use of analogies and metaphors; loosening rigid stimulus functions with cognitive
defusion techniques). This link allows therapists to facilitate an expansion of a client’s
psychological flexibility or behavioral repertoire (see Blackledge & Drake, 2013). Indeed,
there are putative claims that a therapy mainly based on RFT, known as Relational Frame
Therapy (Törneke, 2010; Villatte, Villatte, & Hayes, 2015), might feasibly be developed.
Accordingly, ACT (which, admittedly continues to grow in strength and popularity regardless)
and Relational Frame Therapy would benefit from a similarly strong empirical base of basic and
RFT NOTATION FOR BASIC RESEARCH 6
applied research as that found in traditional behavior therapy (Blackledge & Drake, 2013;
Dymond et al., 2013; Guinther & Dougher, 2015).
Middle-Level Terms
Middle-level terms (i.e., mid-level terms) are terms that appear to have face validity on
the surface as technical operationally defined scientific terms in the clinical literature, but in fact
are nontechnical terms (see Barnes-Holmes et al., 2016, for a thorough overview) because they
do not help provide a precise functional account of clinical problems. In other words, middle-
level terms might appear to be based in solid theoretical grounding, but they are regarded as
nontechnical as they did not emerge, or were generated, from basic empirical research. Barnes-
Holmes et al. helpfully provided examples of what might be considered a low-level term that
emerged directly from basic scientific data (e.g., reinforcement) and a high level term that is
somewhat abstract and atheoretical (e.g., attention). Middle-level terms in ACT include the six
components of psychological flexibility (acceptance, cognitive defusion, self-as-context, present-
moment awareness, values clarification, and committed action), and the broad overarching
consrtruct of psychological flexibility itself. The clinical literature typically treats the
components of psychological flexibility and their interactions as functional behavioral processes
(Barnes-Holmes et al., 2016). However, the use of such terminology in ACT and putative RFT
accounts of problematic clinical behavior is an issue that is of current concern and debate (e.g.,
see Barnes-Holmes et al., 2018; Villatte et al., 2015). Indeed, in a review of Villatte et al.’s
(2015) depiction of the relationship between ACT and RFT, Barnes-Holmes et al. (2018)
highlighted their concerns with mixing technical and nontechnical terms in attempting to account
for clinical phenomena. Mixing technical and nontechnical terms may give a false impression
that all of the terms used have been operationally defined through experimentation. It should be
RFT NOTATION FOR BASIC RESEARCH 7
noted here, however, that Hayes, Barnes-Holmes, and Wilson (2012) have openly acknowledged
the difficulty for ACT’s middle-level terms to ever truly become, or be considered, basic
functional technical terms, “. . . none of these are technical terms; none have the same degree of
precision, scope, and depth of classical behavioral principles such as ‘reinforcement’, nor of
theorertical RFT concepts such as the ‘transformation of stimulus functions. . .’” (p. 7; see also
Barnes-Holmes et al., 2016).
Technical Notation
One tool presented in early RFT research (e.g., Steele & Hayes, 1991) that might be
useful to revisit and revise, due to its potential benefit in helping researchers to become more
precise and technical, is technical notation. Technical notation is used to achieve logical
precision and clearer communication in subjects such as mathematics (see Peltomäki &
Salakoski, 2004), computer science (Paternò, Mancini, & Meniconi, 1997), and even
nanotechnology research (Leisner, Bleris, Lohmeuller, Xie, & Benenson, 2010). Notation
appeared in some early texts presenting the core tenets of RFT, notably Hayes et al. (2001) and
Steele and Hayes (1991), demonstrating that early founders of RFT supported the utility of
technical notation. RFT notation is used to highlight contexts which might be used to predict and
influence behavior with precision, scope, and depth. Previous appearances of this technical
notation (e.g., Hayes et al., 2001; Steele & Hayes, 1991) may have appeared to be more arcane
than functional. In recent years, it has not appeared in many publications as a result. However,
now that researchers are investigating increasingly complex domains within basic RFT (e.g.,
Perez, Fidalgo, Kovac, & Nico, 2015), such as analogy (e.g., McLoughlin & Stewart, 2017),
technical notation may help researchers to hypothesize about, explain, and explore such complex
RFT NOTATION FOR BASIC RESEARCH 8
AARR with increased precision. A compilation of key notation that may be of use to both
experimenters and theorists within the field of RFT can be found in Table 1.
[Table 1 here]
Given that research has indicated that cognition is relational in nature (e.g., Cassidy,
Roche, & Hayes, 2011; O’Hora et al., 2008), this notation syntax allows for a concise
articulation of key concepts and hypotheses about AARR. Below, we describe some of the core
features of language and cognition using notation.
Notation in Context
Mutual Entailment
Crel (A rx B) ||| (B ry A)
The above notation indicates that within a given context (Crel), if an organism has learned
to treat the event A as having a relation (rx) with B, then (|||) the organism should be able to
derive that B is related to A in some way (ry). One particular instance of mutual entailment is
when the A:B relation is one of sameness. The relation of sameness is symmetrical, and thus it is
possible to specify that Crel (A rs B) ||| (B rs A), where “rs” is a relation of sameness. See Table 1
for a full summary of the notation used within this text. Table 2 illustrates possible variations of
rx” notation in relation to some of the more commonly cited patterns of AARR.
[Table 2 here]
Combinatorial Entailment
Crel (A rx B); (B rx C) ||| (A rx C); (C ry A)
This notation illustrates that in a specific context (Crel), if an organism has learned to treat
the event A as having a relation (rx) with B, and the event B as having a relation (rx) with C, then
RFT NOTATION FOR BASIC RESEARCH 9
(|||) the organism should be able to derive that A is related to C in the same way as A:B (rx), and
the mutually entailed relation (C ry A).
This general pattern of AARR only applies to transitive relations (e.g., Slattery, Stewart,
& O’Hora, 2011), for example larger/smaller, before/after, same/opposite, and so on (Johnson-
Laird, 2010). There are indeed stimulus relationships dictated by the verbal community that do
not necessarily lead to combinatorial entailment and these are labelled “intransitive. For
example, if A has met B and B has met C, it would not necessarily follow that A has met C.
Using notation, this could be stated as:
Crel (A rxi B); (B rxi C) |||
Here, i indicates that the relationship is intransitive.
Despite the illogicality of deriving (A rx C) when considering an intransitive relationship,
humans may still derive it. This overgeneralization error could in fact underpin some cognitive
biases. For example, if Person A harms Person B, and Person B harms Person C, then Person C
is not necessarily the victim of Person A. In some way, the existence of this intransitivity
phenomenon presents a considerable theoretical and empirical challenge for RFT that is not
readily accountable for in current formulations of the theory.
Likewise, if Class A and Class B are equivalence classes of people related via an
asymmetrical relation (i.e., hierarchically) then the effect of Class A on Class B (e.g.,
oppression) does not necessarily hold for individual members (Persons A and B), as transitive
class containment might suggest (see Slattery & Stewart, 2014). Such patterns of deriving false
information may have an association with certain psychological disorders, for example,
psychosis, anxiety, paranoia, and schizophrenia (see Stewart, Stewart, & Hughes, 2016).
RFT NOTATION FOR BASIC RESEARCH 10
Further, there are situations in which (A rx B) and (B rx C) can never derive (A rx C). For
example, if A is the mother of B, and B is the mother of C, it follows that A can never be the
mother of C. This is known as an antitransitive relationship, which can be notated as:
Crel (A rxa B); (B rxa C) ||| /(A rx C)
Where a denotes anti-transitivity, and / denotes the lack of a derived relationship. In this
instance, it would be functional not to derive (A rx C). As mentioned previously, RFT does not
readily account for this type of relation. As (we hope) RFT grows to account for these
unexamined types of relationships, it would be useful to use notation, because various kinds of
relationships can be written in such notation easily.
Accordingly, basic transitive combinatorial relations would be written in notation as:
Crel (A rxt B); (B rxt C) ||| (A rxt C); (C ryt A)
Here, t denotes transitivity.
Networks containing transitive relationships quickly expand with the addition of further
stimulus relationships. For example, consider that training three relationships (A rxt B), (B rxt C),
(C rxt D) combinatorially entails as such:
Crel (A rxt B); (B rxt C); (C rxt D) ||| (A rxt C); (C ryt A); (B rxt D); (D ryt B); (A rxt D); (D ryt A)
If we train a five-node network with four stimulus relations A-B-C-D-E, this combinatorially
entails six relationships (if we decline to count the mutually entailed relations of those directly
trained). If we take into account the mutual entailments of each of the combinatorially derived
relations, 12 stimulus relations are derived:
Crel (A rxt B); (B rxt C); (C rxt D); (D rxt E) ||| (A rxt C); (C ryt A); (A rxt D); (D ryt A); (A rxt E); (E
ryt A); (B rxt D); (D ryt B); (B rxt E); (E ryt B); (C rxt E); (E ryt C);
This notation demonstrates the generativity inherent in relational behavior.
RFT NOTATION FOR BASIC RESEARCH 11
Transformation of Functions
Cfunc [Crel {(A rx B; B rx C) ||| (A rx C; C ry A)}; {Af1; Bfn; Cfn} ||| (Bf2; Cf3)]
Transformation of stimulus functions occurs when contextual contingencies select a
behavioral function or value. This statement says: In a given context (Crel), if the organism has
derived a relation (A rxt B; B rxt C ||| (A rx C; C ry A) and a nonrelational function of a stimulus in
that relational network (e.g., Af1) has been established in the organism’s behavioral repertoire
(Cfunc), then (|||) the organism will derive the relative functions of stimuli participating in the
relational response (i.e., the functions of B and C are modified based on the relations in which
they participate).
Analogical Relations
Crel (A rx B); (C rx D) ||| (A:B) rs (C:D)
This notation specifies that within a particular context (Crel), if two relations (i.e., A:B
and C:D) are of the same type (i.e., rx and rx), then a relation of coordination or functional
equivalence (rs) might be derived between these relations.
Differentiated Relations
Crel (A rx B); (C ry D) ||| (A:B) rd (C:D)
The above notation expresses that within a given context (Crel), if two relations (i.e., A:B
and C:D) are of differing types (e.g., rx and ry), then a relation of distinction (rd) might be derived
between these relations.
It is possible to use notation to identify increasingly complex kinds of relational
responding that might be tested and/or trained. For example:
Crel (A rs B); (C ro D) ||| (A:B) rd; ro (C:D)
RFT NOTATION FOR BASIC RESEARCH 12
The above notation illustrates that within a specific context, if an organism treats two
stimuli (A and B) as being the same (rs), and two more stimuli (C and D) as being opposite (ro),
then it might be derived that (|||) the relation between the first relation (A:B) and the second
(C:D) is one of difference (rd), specifically opposition (ro). It should be noted that if notation was
not used for the examples above, it would likely have taken hundreds more words and dozens of
potentially ambiguous or easily misinterpretable diagrams to explain the stimulus relations in
question.
Some More Future Studies
It is possible to include a plethora of relations in studies of complex cognition. For
example, below we include hypotheses pertaining to differentiating rd from ro, and rb (before)
from ra (after):
Crel (A rd B); (C ro D) ||| (A:B) rd / ro (C:D)
Crel (A rb B); (C ra D) ||| (A:B) rd; ro (C:D)
The utility of establishing such fine experimental control over AARR is an empirical
matter (e.g., these kinds of skills trained to fluency may be useful for mathematics and other
forms of higher logic). In this instance, the term behavioral fluency refers to the combination
of precise and swift responding that is considered to be synonymous with expert performance or
mastery of a behavioral repertoire (Binder, Haughton, & Bateman, 2002; McTiernan, Holloway,
Healy, & Hogan, 2015; Ramey et al., 2016). The concision offered by such notation may allow
for clearer prediction and influence over increasingly complex behaviors in future, including
behaviors that are perhaps currently beyond our species.
It may be possible to investigate the derivation of relations within yet more complex
relations. For example, below are two competing hypotheses asking whether individuals will
RFT NOTATION FOR BASIC RESEARCH 13
derive a “more than” relation to be opposite a “less than” relation, or simply consider them
distinct.
Crel (A rm B); (C rl D) ||| (A:B) rd (C:D)
Crel (A rm B); (C rl D) ||| (A:B) ro (C:D)
There are many other nonsymmetrical relations that could be similarly related. For
example, the hypotheses below ask: is “before” opposite to “after,” or just different?
Crel (A rb B); (C ra D) ||| (A:B) rd (C:D)
Crel (A rb B); (C ra D) ||| (A:B) ro (C:D)
These may have useful applications for the understanding of complex phenomena. For
example, RFT considers “the self” to be a nexus of many established relational networks. To
differentiate relational networks may therefore be an important skill underlying the ability to
differentiate among different “selves.” Learning to do this expressively (e.g., McLoughlin &
Stewart, 2017, modeled this behavior of differentiating relational networks receptively using the
Relational Evaluation Procedure) could constitute an operationalized account of “I–you”
relational framing. With the inherent complexity that comes with such novel questions, notation
could ensure the technicality and precision of hypotheses and experimental procedures, while
simultaneously allowing them to be communicated concisely.
Likewise, complex relational repertoires, such as that of hierarchical classification are
amenable to RFT notation. For example, below we include a rudimentary notation of hierarchical
classification:
Crel (A1 rp B; A2 rp B; B rp C) ||| (A1 rs A2; A1 rp C; A2 rp C; C rc A1; C rc A2; C rc B; B rc A1; B
rc A2)
RFT NOTATION FOR BASIC RESEARCH 14
This notation outlines that the stimuli A1 and A2 are part of the stimulus class B, which
is part of the stimulus class C. From this information, an individual can derive a degree of
functional sameness between stimuli A1 and A2, while simultaneously deriving that the stimuli
A1 and A2 are part of the stimulus class C. This also leads to further derivations including that
stimulus class C contains stimuli A1, A2, and B, while the stimulus class B contains the stimuli
A1 and A2. The complexity of these relational networks are further outlined when the
transformation of stimulus function is considered.
Cfunc [Crel {(A rc B; B rc C) ||| (A rc C; C rp A; C rp B; B rp A)};
If we derive “A contains B, and B contains C” for functional purposes, then
{Af1; Bfn; Cfn} ||| (Bf2; Cf3);
That is, if we know the functions of superordinate class A, they will change the functions of
subordinate classes B and C. Furthermore,
{Afn; Bf1; Cfn} ||| (Afn; Cf2);
If we only knew the function of class B, it would transform the functions of subordinate class C
and not superordinate class A. Finally,
{Afn; Bfn; Cf1} ||| (Afn; Bfn)]
If we only knew the function of subordinate class/stimulus C, then it does not necessarily tell us
about the functions of its superordinate classes A and B. That is, we might expect all of the
functions of the containing network to transform the functions of the member network, but the
member network should not transform the functions of the class. This is, of course, a testable
hypothesis. It is also possible that the salient functions of a group are abstractions of what’s
common across its constituents, which might mean that individual members transform functions
of the group as a whole. This can be good, because it is useful to know the truth criteria for
RFT NOTATION FOR BASIC RESEARCH 15
category membership; categories help us to simplify the world around us. In other cases,
perhaps, this may not be so adaptive. For example, I might think that a key feature of what it
means to be a RAEF (superordinate group) is that they have DOBs. Then I might hear about
individual RAEFs (named Jeff, Toby, and Ben): Ben explains things condescendingly; Toby is
unfaithful to his partner; Ben is prejudiced against non-RAEFs. Being mean and undesirable is
common across Jeff, Toby, and Ben, and so it is possible that individuals transform the functions
of groups for the worse. In other words, I might now generalize from these exceptional
exemplars to say that RAEFs are mean-spirited (or worse), and conclude that we need to create
quotas of non-RAEFs to keep them in check. The problem here would be that any person who
has a DOB and, therefore, fits into the category “RAEF,” or demonstrates any otherwise
advantageous trait associated with being RAEF-like, may be stereotyped as being like Jeff, Toby,
and Ben. This would be a logical non sequitur, and potentially obscure the fact that, in some
contexts, it’s good to be RAEF-like. If the hypothesis in the notation above were to be rejected in
an experiment (i.e., if participants derived functions of a category that don’t generally apply to
it), the errors may be indicative of a deficit in hierarchical AARR abilities, and so training these
generalizable patterns of behavior could be justified. Indeed, there are precedents in the literature
for training both simple AARR (e.g., Cassidy et al., 2011) and more complex AARR repertoires
(e.g., McLoughlin, Tyndall, & Pereira, 2018; see also Guinther, 2018).
We may also refine more basic assumptions using empirical tests. For example, does
transformation of stimulus functions always happen as expected across a combinatorial relation?
It is possible to conceive of an instance when it does not.
Crel (A rx B); (B rx C) ||| (A rx C); (C ry A)
RFT NOTATION FOR BASIC RESEARCH 16
In the above account of combinatorial entailment, the relation between A and B (rx) is the
same as the B:C relation. This entails that the A:C relation should be the same as the A:B and
B:C relations, apart from by order of magnitude. However, as has been shown, a relationship
may be transitive or intransitive, and combinatorial entailment should only occur in the former.
Perhaps this explains why some participants do not always combinatorially entail in studies of
this nature (e.g., Quinones & Hayes, 2014). A future experiment could examine whether
participants could be influenced to treat relationships as transitive or intransitive. For example,
participants could be repeatedly trained on relationships such as:
Crel (A rxa B); (B rxa C) ||| /(A rx C)
or
Crel (A rxi B); (B rxi C) |||
If participants could be so influenced, it may be possible to train participants not to
combinatorially entail so readily, which would lead to patterns of relational framing that are
more selectively applied, and in doing so this could prevent the spread of negative stimulus
functions through overgeneralization and reduce cognitive errors.
Concluding Remarks
Of the few principles in psychology, behavioral selection by consequences is arguably
the most fundamental offered by the field. There appears to be somewhat of a converging
consensus from various fields, including behavioral psychology (Hayes et al., 2001), cognitive
psychology (Halford, Wilson, & Phillips, 2010), and linguistics (Garcia, 2015), that indicates
that language and cognition are relational in nature, with increasingly complex language and
cognition involving the utilization of progressively complex relational responses (see Barnes-
Holmes et al., 2005; Cassidy et al., 2011; Cassidy, Roche, Colbert, Stewart, & Grey, 2016;
RFT NOTATION FOR BASIC RESEARCH 17
Hayes & Stewart, 2016; Moran, Walsh, Stewart, McGhee, & Ming, 2015; O’Hora, Barnes-
Holmes, Roche, & Smeets, 2004; Stewart, Barnes-Holmes, & Roche, 2004). It should be
acknowledged that RFT as a functional-analytic account of human language and cognition
(Hayes & Barnes, 1997) has shed a considerable amount of light on complex relational
processing in a relatively short period of time. As this field develops, it may become difficult to
articulate hypotheses in-text as the kinds of high-level operant responses trained and tested
incrementally become more complex.
In this short article, we have proposed that the notation style appearing in early RFT
literature may be useful in that regard. In addition, we have attempted to illustrate its utility using
multiple exemplars and have provided a “key” (see Tables 1 and 2) regarding some useful
notation for formulating hypotheses for exploring AARR. It is salient that the use of such
notation might also conceivably assist in the design of experiments that may help to counteract
research that claims empirical findings in RFT studies can generally be accounted for by
appealing to contextual control of equivalence relations alone (e.g., Sidman, 1994; Alonso-
Álverez & Pérez-González, 2017). For example, Alonso-Álvarez and Pérez-González (2017)
proposed that prior RFT empirical demonstrations of derivations of Same and Opposite
relations (e.g., Dymond & Barnes, 1995; Dymond, Roche, Forsyth, Whelan, & Rhoden, 2007;
Whelan & Barnes-Holmes, 2004) could also be explained by contextual control over equivalence
and nonequivalence relations, respectively. Although Alonso-Álvarez and Pérez-González’s
proposal might have immediate appeal in terms of simplicity and parsimony, it is difficult to
conceive how their position might potentially account for many of the more complex AARR
relations that the use of RFT’s technical notation might predict.
RFT NOTATION FOR BASIC RESEARCH 18
For translational RFT-to-practice researchers targeting complex repertoires such as
perspective-taking or psychological flexibility, perhaps the challenge of operationalizing such
concepts in more technical terms might help them to identify relevant manipulable behavioral
contingencies. However, as noted above, at present middle-level terms such as “psychological
flexibility” have not yet been clearly operationalized in technical terms, but in colloquial terms
(Barnes-Holmes et al., 2016). This is not to say that mid-level terms such as these are not useful
in certain contexts, but they may warrant further exploration given that these are concepts upon
which many practitioners (e.g., ACT therapists) base their practice, rather than principles that
survive through basic experimentation.
In summary, scientists studying AARR may be able to use this notation to communicate
increasingly complex hypotheses with precision, as complexities in experiments evolve.
Naturally, this notation remains one of the more arcane aspects of RFT and may not have initial
appeal to a casual or applied practice readership. It is important to acknowledge that from an
RFT perspective all definitions will be judged ultimately by their utility. Thus, our goal is not to
test RFT predictions per se or even provide tools for assessing the coherence of the definitions
with logical notation but rather to put notation on RFT as it was originally proposed.
Nonetheless, technical notation can prove extremely useful to basic RFT researchers for the
formulation of succinct hypotheses, particularly in relation to complex cognition. Technical
notation may also provide clarity in terms of communicating AARR research to those who are
inclined to engage with RFT at the basic science level. This piece is intended to function as a
nondefinitive, but useful resource in that regard.
Compliance with Ethical Standards
RFT NOTATION FOR BASIC RESEARCH 19
Disclosure of Conflicts of Interest: On behalf of all the authors the corresponding author
confirms that no author has a conflict of interest to declare.
Funding: The study was not supported by any grant funding from any institution or
organization.
Ethical Approval: Not applicable as not an empirical study paper.
RFT NOTATION FOR BASIC RESEARCH 20
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RFT NOTATION FOR BASIC RESEARCH 27
Table 1
Relational Frame Theory Notation
Syntax
Meaning
Crel
Contextual contingencies selecting a relational response
Cfunc
r
f
Contextual contingencies selecting a behavioral function
A relation
A stimulus function
fn
A:B
The unspecified stimulus function “n” (superscript, specified via numeric
characters*)
An undefined relation between two stimuli, “A” and “B”; “A is to B”
rx
ry
The undefined relation “x” (specified via alpha characters)
An undefined relation that is not necessarily “x,” only used after “rx
|||
“Entails,” or “predicts”
X
The stimulus “X”
Xfn
The unspecified function of stimulus “X” (superscript, specified via
numeric characters)
;
“And”
/
“Not,” or “but not” (e.g., “A rd / ro B” means “A is different from but not
opposite to B”)
RFT NOTATION FOR BASIC RESEARCH 28
Table 2
Notation for Common Patterns of Arbitrarily Applicable Relational Responding
Syntax
Meaning
rs
rd
A coordinate (functional sameness) relation
A distinction (functional difference) relation
ro
rb
ra
An opposition relation
A “before” temporal relation
An “after” temporal relation
rm
rl
A “more than” (or “greater than”) comparison relation
A “less than” comparison relation
rp
A “part of” hierarchical relation
rc
rx+n
A “contains” hierarchical relation
Used to emphasize comparative relationality (e.g., “rm+1” could mean an
“even more than” relation)
rxi
Specifies that this particular relational cue “x” is intransitive
rxa
Specifies that this particular relational cue “x” is antitransitive
rxt
Specifies that this particular relational cue “x” is transitive
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