3.3 Stimulus Control, Equivalence, and Elementary Verbal Operants

Stimulus Control and Differential Reinforcement

In applied behavior analysis, behavior does not occur in an environmental vacuum. Stimulus control is defined as the phenomenon in which a response is emitted with a higher frequency, shorter latency, longer duration, or greater amplitude in the presence of an antecedent stimulus than in its absence (Terrace, 1966; Cooper, Heron, & Heward, 2020).

Stimulus control is established through differential reinforcement:

• In the presence of a specific antecedent stimulus (Discriminative Stimulus, or $S^D$), the response is consistently followed by reinforcement ($S^D \to R \to S^R$).
• In the presence of alternative or irrelevant stimuli (Stimulus Delta, or $S^\Delta$), the response is placed on extinction ($S^\Delta \to R \to \text{Extinction}$) or lower-density reinforcement.
• In the presence of a stimulus correlated with punishment ($S^{\Delta p}$), the response has historically produced an aversive consequence.

Over repeated trials, the organism learns to discriminate between the $S^D$ and $S^\Delta$, resulting in tight stimulus control where the behavior occurs almost exclusively in the presence of the $S^D$.

Simple vs. Conditional Stimulus Control

In a simple discrimination, one stimulus (the $S^D$) signals that a response will be reinforced: saying "dog" when shown a dog, or stopping at a red light. In a conditional discrimination, the function of one stimulus depends on another stimulus. In matching-to-sample, which comparison is correct depends on the sample: touching the dog picture is reinforced only when the instruction is "dog." Receptive identification, reading comprehension, and equivalence-based instruction all depend on conditional discriminations, which are taught step by step in the section on teaching discriminations.

Faulty Stimulus Control and Stimulus Overselectivity

When designing instructional interventions, clinicians must monitor for faulty stimulus control, which occurs when an unintended, irrelevant feature of the antecedent stimulus controls the response. For example, if a child is taught to identify a flashcard of a cow, but the clinician always points to the card or the card has a distinctive smudge in the upper corner, the child may respond to the finger prompt or the smudge rather than the critical morphological features of the cow. A related clinical phenomenon is stimulus overselectivity, frequently observed in autism spectrum disorder, where the individual's responding is disproportionately controlled by a single, narrow, often minor element of a complex stimulus array (e.g., attending only to the color of a shoe while ignoring its form and size).

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Stimulus Generalization vs. Stimulus Discrimination

• Stimulus Generalization: Occurs when an operant response that has been reinforced in the presence of a specific $S^D$ is emitted in the presence of novel stimuli that share physical or topographical characteristics with that $S^D$.
• Stimulus Discrimination: Occurs when an individual responds differentially to different stimuli, emitting the behavior in the presence of the $S^D$ while withholding it in the presence of similar but non-reinforced stimuli ($S^\Delta$).

The Generalization Gradient

The balance between generalization and discrimination is graphically depicted using a stimulus generalization gradient (Guttman & Kalish, 1956). In an experiment, an organism is reinforced for responding to a specific stimulus dimension (e.g., a yellow-green light of 580 nanometers). During non-reinforced test probes, lights of various wavelengths (550 nm to 620 nm) are presented, and response rates are plotted.

• Steep Gradient: A steep, sharply peaked curve indicates that responding drops off rapidly as test stimuli deviate from the original $S^D$. This demonstrates a high degree of stimulus discrimination and tight stimulus control.
• Flat Gradient: A broad, flat curve indicates that responding continues at high rates across a wide spectrum of physical variants. This reflects a high degree of stimulus generalization and minimal stimulus control.

Concept formation requires both processes: stimulus generalization within a stimulus class (e.g., recognizing that terriers, poodles, and golden retrievers are all "dogs") and stimulus discrimination between stimulus classes (e.g., discriminating between dogs and cats).

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Stimulus Equivalence: Derived Relational Responding

In 1971, Murray Sidman revolutionized behavior-analytic approaches to complex language and cognition by discovering stimulus equivalence (Sidman, 1971, 1994). Stimulus equivalence describes the emergence of accurate, untaught, and unreinforced derived relations among stimuli following the direct reinforcement of a limited subset of conditional relations.

To establish an equivalence class, three defining mathematical and behavioral properties must be demonstrated through rigorous probe trials without reinforcement:

1. Reflexivity (Generalized Identity Matching)

In the absence of any prior training or reinforcement, an individual matches a stimulus to itself ($A = A$).

• Test Probe: Presented with a sample stimulus consisting of a physical picture of a dog ($A$), the individual selects an identical picture of a dog ($A$) from a comparison array consisting of a dog, a bicycle, and a cup ($A = A$).

2. Symmetry (Bidirectionality / Reversibility)

After direct training and reinforcement of a conditional relation between stimulus $A$ and stimulus $B$ ($A \to B$), the individual independently demonstrates the reverse relation ($B \to A$) without direct reinforcement.

• Direct Training: The practitioner vocally says "dog" (auditory stimulus $A$) and reinforces the learner for selecting the printed picture of a dog (visual stimulus $B$).
• Derived Symmetry Probe: The practitioner presents the picture of a dog ($B$) and asks the learner to identify or vocally produce the spoken word "dog" ($A$). When the learner emits $B \to A$ without explicit training, symmetry is demonstrated.

3. Transitivity (Untrained Derived Combined Relation)

After direct training of two distinct conditional relations that share a common nodal stimulus—specifically, training $A \to B$ and training $B \to C$—the individual demonstrates the emergent, untrained relation $A \to C$, as well as the combined symmetric-transitive relation $C \to A$, in the complete absence of direct reinforcement.

• Direct Training 1: Spoken word "dog" ($A$) $\to$ Picture of a dog ($B$).
• Direct Training 2: Picture of a dog ($B$) $\to$ Printed text "D-O-G" ($C$).
• Transitivity Probe: Spoken word "dog" ($A$) $\to$ Printed text "D-O-G" ($C$).
• Symmetric-Transitivity Probe (Equivalence): Printed text "D-O-G" ($C$) $\to$ Spoken word "dog" ($A$).

When reflexivity, symmetry, and transitivity are empirically confirmed, stimuli $A$, $B$, and $C$ form an equivalence class ($[A, B, C]$). They become functional substitutes for one another, providing the foundation for reading comprehension, symbolic communication, mathematical problem-solving, and abstract thinking.

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Skinner's Functional Analysis of Verbal Behavior

In his seminal 1957 treatise Verbal Behavior, B.F. Skinner bypassed traditional linguistic, grammatical, and structural classifications of language. Skinner defined verbal behavior as behavior reinforced through the mediation of another person whose behavior has been explicitly conditioned by the practices of a verbal community (Skinner, 1957).

Rather than analyzing what words mean (mentalism) or how sentences are grammatically arranged (syntax), Skinner analyzed the functional controlling variables governing the emission of verbal operants: their antecedent conditions (motivating operations, nonverbal discriminative stimuli, verbal discriminative stimuli) and their consequences (specific reinforcers vs. generalized conditioned reinforcement).

Critical Analytic Dimensions

To classify Skinner's verbal operants, behavior analysts evaluate two formal relationship criteria between the antecedent verbal stimulus and the verbal response product:

1. Point-to-Point Correspondence: Occurs when the beginning, middle, and end of the antecedent verbal stimulus match the beginning, middle, and end of the verbal response. (For example, hearing the word "CAT" and repeating "C-A-T"; or seeing the printed word "CAT" and vocalizing "k-ae-t"). Point-to-point correspondence does not require identical physical modality.
2. Formal Similarity: Occurs when the antecedent verbal stimulus and the verbal response product share the same physical modality (e.g., both are auditory-vocal, or both are visual-written) AND physically resemble one another. (For example, hearing "HELLO" and vocalizing "HELLO" has formal similarity; reading printed text aloud lacks formal similarity because the stimulus is visual and the response product is acoustic).

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The Elementary Verbal Operants

1. Mand

• Antecedent Control: An establishing operation (EO) or motivating operation (deprivation, aversive stimulation, pain).
• Response: A vocal, signed, or graphic request.
• Consequence: A specific, characteristic reinforcer that directly addresses the active motivating operation.
• Significance: The mand is the only verbal operant that directly benefits the speaker. Because it is controlled by the speaker's momentary motivational state, it is the first verbal operant taught in early language intervention (Sundberg & Partington, 1998).
• Example: An individual has been deprived of water for 4 hours (EO: thirst) $\to$ emits vocal response "Water" $\to$ receives a cup of cold water ($S^R+$).

2. Tact

• Antecedent Control: A non-verbal discriminative stimulus ($S^D$) (an object, person, event, action, internal sensation, or environmental relation accessed through vision, hearing, touch, taste, or olfaction).
• Consequence: Generalized conditioned social reinforcement (GCSR) (praise, acknowledgment, nodding, attention).
• Significance: Tacts name, label, or describe the physical environment, benefiting the listener by providing information about the surroundings.
• Example: Seeing a red cardinal fly past the window (nonverbal visual $S^D$) $\to$ child says "Birdie!" $\to$ parent smiles and says "Yes, that's a pretty red cardinal!" (GCSR).

3. Echoic

• Antecedent Control: A vocal verbal discriminative stimulus.
• Relationship: Possesses both point-to-point correspondence and formal similarity (both are vocal-auditory).
• Consequence: Generalized conditioned social reinforcement (GCSR).
• Significance: Serves as the behavioral stepping stone for shaping articulated speech topographies and teaching all other complex verbal operants.
• Example: Speech therapist says "Apple" $\to$ learner vocally repeats "Apple" $\to$ therapist delivers praise: "Great repeating!" (GCSR).

4. Intraverbal

• Antecedent Control: A verbal discriminative stimulus (vocal, written, or signed).
• Relationship: Does NOT possess point-to-point correspondence with the antecedent stimulus.
• Consequence: Generalized conditioned social reinforcement (GCSR).
• Significance: Underlies human conversation, answering questions, associative thought, reciting facts, and social dialogue.
• Example: Teacher asks "What color is the grass?" $\to$ student responds "Green" $\to$ teacher says "That's right!" (GCSR).

5. Textual

• Antecedent Control: A written/printed verbal discriminative stimulus.
• Relationship: Possesses point-to-point correspondence (letters map to phonemes), but NO formal similarity (stimulus is visual print; response product is auditory speech).
• Consequence: Generalized conditioned social reinforcement (GCSR).
• Significance: The behavioral definition of reading text aloud (note that textual responding does not inherently require reading comprehension; comprehension requires stimulus equivalence).
• Example: Seeing the printed word "EXIT" on a sign $\to$ vocalizing "Exit" $\to$ listener confirms "Correct."

6. Transcription (Taking Dictation / Copying Text)

• Antecedent Control: A verbal discriminative stimulus.
• Relationship: Possesses point-to-point correspondence.
  • When copying written text (visual to visual), it possesses both point-to-point correspondence and formal similarity.
  • When taking dictation (hearing a spoken word and writing it down), it possesses point-to-point correspondence, but NO formal similarity.
• Consequence: Generalized conditioned social reinforcement (GCSR).
• Example: Teacher vocally dictates the spelling word "SPEECH" $\to$ student writes letters S-P-E-E-C-H on the paper $\to$ receives a star stamp (GCSR).

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Skinner's Elementary Verbal Operants Matrix

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Pure vs. Impure Verbal Operants in Clinical Instruction

In natural environments and early intervention, verbal behavior rarely occurs in completely isolated, "pure" forms. Practitioners frequently observe impure verbal operants, which occur under multiple antecedent controlling variables:

• Mixed Mand-Tact (Multiple Control): A child is thirsty (EO), sees a cup of juice on the kitchen counter (nonverbal $S^D$), and says "Juice." The response is controlled simultaneously by the motivating operation and the nonverbal stimulus.
• Prompted Mand (Intraverbal Mand): The clinician asks "What do you want?" (verbal $S^D$) while the child reaches for a toy (EO). The child says "Bubbles." The response is controlled by both the verbal antecedent and the EO.

To establish pure verbal repertoires, clinicians use systematic transfer of stimulus control procedures. For example, to establish a pure mand, the clinician fades out the intraverbal prompt ("What do you want?") and the visual presence of the item, until the mand is evoked solely by the client's internal motivating operation.