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R R Saunders

Publications and source records attributed to R R Saunders.

7 recordsLinked to original sources
PubMed1992

The nonequivalence of behavioral and mathematical equivalence.

Sidman and his colleagues derived behavioral tests for stimulus equivalence from the axiom in logic and mathematics that defines a relation of equivalence. The analogy has generated abundant research in which match-to-sample methods have been used almost exclusively to study interesting and complex stimulus control phenomena. It has also stimulated considerable discussion regarding interpretation of the analogy and speculation as to its validity and generality. This article reexamines the Sidman stimulus equivalence analogy in the context of a broader consideration of the mathematical axiom than was included in the original presentation of the analogy and some of the data that have accumulated in the interim. We propose that (a) mathematical and behavioral examples of equivalence relations differ substantially, (b) terminology is being used in ways that can lead to erroneous conclusions about the nature of the stimulus control that develops in stimulus equivalence experiments, and (c) complete analyses of equivalence and other types of stimulus-stimulus relations require more than a simple invocation of the analogy. Implications of our analysis for resolving current issues and prompting new research are discussed.

Animals↗
PubMed1991

The role of instructions in the transfer of ordinal functions through equivalence classes.

In two experiments, adult subjects completed match-to-sample training and testing to establish four equivalence classes of four figures each. Then the subjects were taught one three-position sequence consisting of one stimulus from Class 1, one from Class 2, and one from Class 3. Inclusion of Class 4 stimuli in sequences was never reinforced, but two different stimuli from Class 4 appeared as distractors on each sequence trial. Tests assessed whether subjects would produce novel three-position sequences composed of members of Classes 1 through 3 that had not been used in sequence training. Three subjects in Experiment 1 received instructions about the match-to-sample and sequencing tasks, in addition to training contingencies. All 3 demonstrated equivalence class formation after match-to-sample training. After they were taught one sequence with one member of Classes 1 through 3, none of these subjects produced untrained sequences with other equivalence class members reliably. One additional sequence was trained directly; thereafter 1 subject showed some evidence of transfer of the trained ordinal functions across the remaining members of the equivalence classes, but the other 2 did not. Following a review of equivalence class training and testing and a review of the original sequence training, all 3 subjects produced most of the predicted, untrained sequences on tests. Experiment 2 replicated Experiment 1 with 2 adults but omitted all instructions except the minimal ones necessary to initiate responding. Unlike the subjects in Experiment 1, both of these subjects demonstrated virtually complete transfer of ordinal functions through the equivalence classes after direct training on just one sequence composed of one member of Classes 1 through 3.

Adult↗
PubMed1990

Equivalence classes generated by sequence training.

In Experiment 1, 3, adult females were taught with verbal instructions and contingencies to select, in sequence, three arbitrary visual stimuli from an array of five stimuli. After four different sequences were taught, match-to-sample tests assessed emergent conditional relations among all stimuli that had been selected in the same order in the sequences. Subjects' performances indicated development of four stimulus classes, three based on ordinal position and one based on nonselection. Next, match-to-sample training established conditional relations between each of four novel figures and one member of each of the ordinal stimulus classes. Tests confirmed that the classes were equivalence classes, each expanded by one new member. In subsequent sequence tests, the new stimuli were selected in a sequence that was consistent with ordinal class membership. Experiment 2 replicated Experiment 1 with 2 different adult females, but the verbal instructions were omitted. Results were similar to Experiment 1, except that extensive review and retesting were required before expansion of the ordinal classes with the novel figures was observed.

Adult↗
PubMed1990

Long-term stability of equivalence relations in the absence of training or practice.

An adult male with mild mental retardation, whose laboratory history included training in a match-to-sample task on 16 arbitrary relations among 16 visual stimuli and 2 auditory stimuli, had performances that showed the development of 112 additional arbitrary relations that had never been reinforced. In the presented study on 2-year and 3-year follow-up tests for these derived relations, his performances remained stable despite the absence of opportunities to practice these relations between the tests and the absence of explicit feedback during the tests. The similarity to the long-term stability of language was discussed.

Adult↗
PubMed1988

Establishing auditory stimulus control over an eight-member equivalence class via conditional discrimination procedures.

Two eight-member equivalence classes of visual stimuli were established during three phases of a training program. In Phase 1, two training arrangements were compared. In one, 3 subjects were taught on different trials to select from a single pair of comparison stimuli (A1, A2) in response to eight sample stimuli that were trained in pairs (B1, B2; C1, C2; D1, D2; E1, E2). In the second arrangement, subjects were taught to select from four pairs of comparisons (B1, B2; C1, C2; D3, D2; E2, E2) in response to two samples (A1, A2). Training with the single pair of comparison stimuli resulted in the development of equivalence relations (B1C1, B2C2, D1B1, D2B2, B1E1, B2E2, C1D1, C2D2, C1E1, C2E2, D1E1, D2E2, and their reciprocals) between the sample stimuli without direct training of these relations. In the other training arrangement, these relations among the comparison stimuli developed in the performance of 1 subject only. In Phase 2, three new pairs of stimuli (F1, F2; G1, G2; H1, H2) were substituted for three of the original pairs (B1, B2; C1, C2; D1, D2) and the training arrangements for the groups were reversed. Following training, the performances that showed equivalence relations on the probes in the first phase also showed equivalence relations in the second phase. If such relations did not develop in the first phase, they did not do so in the second phase. In Phase 3, relations between stimuli across the two previous phases (e.g., B1F1, B2F2, B1G1, B2H2, C1F1, etc.) were investigated. The 4 subjects whose performances showed the development of these relations were taught to select one stimulus from each class (E1 and E2) in response to a verbal label (I1 and I2) and then were tested to see if the verbal label controlled responding to the remaining members of the class (e.g., I1A1, I2A2, I1B1, I2B2, etc.). For 3 subjects, this generalized control occurred; for the 4th, generalization occurred only after verbal training with a second pair of visual stimuli (F1 and F2). In retests several months later, these auditory-visual relations were found to be intact or, if not, were recovered without direct training.

Adolescent↗
PubMed1988

The merger and development of equivalence classes by unreinforced conditional selection of comparison stimuli.

Three experiments assessed the likelihood that subjects with histories of equivalence class development would respond conditionally on new discriminations in the absence of differential consequences for responses. In the first two experiments, two groups of subjects with different experimental histories, but whose performances showed four equivalence classes, responded on trials without explicit reinforcement involving samples from two of the classes and comparisons from the other two classes, in a two-choice matching-to-sample format. Subjects consistently selected a particular comparison in the presence of a particular sample. Subsequent tests showed the emergence of equivalence relations between stimuli from classes linked by the unreinforced conditional selections. Subsequently, in Experiment II, the subjects' responses in the conditional selection trials were reinforced if the selection was reversed from that made previously. Although reversed selection was maintained, 2 of the 3 subjects continued to perform on equivalence relation trials according to their original unreinforced selections. In the third experiment, these 2 subjects responded on a series of conditional discriminations involving three new pairs of sample stimuli and one new pair of comparison stimuli. No explicit reinforcement followed responses on any trial in this experiment. Subsequent tests for equivalence between sample stimuli revealed the development of two equivalence classes.

Adolescent↗