1990, 53, 345-358
JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR
NUMBER 3
(MAY)
THE EFFECTS OF NODALITY ON THE FORMATION OF EQUIVALENCE CLASSES LANNY FIELDS, BARBARA J. ADAMS, THOM VERHAVE, AND SANDRA NEWMAN THE COLLEGE OF STATEN ISLAND/CUNY AND QUEENS COLLEGE/CUNY A four-member equivalence class (A - B - C - D) can be formed by training AB, BC, and CD. The nodal stimuli, B and C, mediate all of the derivative (transitive and equivalence) relations in the class. The derivative relations AC, CA, BD, and DB are separated by one node, whereas AD and DA are separated by two nodes. How do the number of nodes that separate the stimuli in a derivative relation influence the induction of stimulus control exerted by that relation? Seven college students learned two four-member classes made up of nonsense syllables. After training, all derivative relations were presented repeatedly without informative feedback. Stimulus control exerted by each derivative relation was assessed concurrently. For the 7 subjects, control exerted by the derivative relations increased gradually with repeated presentations. With 6 of the 7 subjects, the one-node relations exerted more control than the two-node relations during the process. However, the disparity between the one- and two-node relations decreased with repeated presentations. Eventually, all derivative relations exerted complete control. The control exerted by derivative relations during induction was inversely related to the number of nodes separating the terms in the derivative relations. These results demonstrate that nodal distance is a determinant of the relatedness of stimuli in equivalence classes. The findings are discussed in terms of remote association, semantic memory networks, and the study of transitive inference. Key words: equivalence class, intervening nodes, derivative relations, remote associations, semantic memory networks, associative distance, nonsense syllables, computer keyboard input, college students
An equivalence class consists of a group of stimuli, all of which become interrelated even though they do not necessarily share any common physical properties (Sidman, 1971). An example of such a class drawn from the realm of organic chemistry consists of the four representations of ethanol: C2H5OH, grain alcohol, liquor, and ethanol. To create a class from a group of N such disparate stimuli, (N - 1) stimulus-stimulus relations must be established by training, with the proviso that each stimulus is used in at least one of the stimulus-stimulus relations (Fields, Verhave, & Fath, 1984). In addition, two different stimuli must be used in each training relation. If the four stimuli in the group are identified
by the letters A, B, C, and D, one way to establish the class is to train the two-term relations AB, BC, and CD, each of which is represented by one of the arrows above the stimulus letters in Figure 1. Each two-term relation is established on a trial-by-trial basis using the conditional discrimination paradigm. For example, during AB training, A is presented as a sample with B as a positive comparison and an unrelated new stimulus (X) as a negative comparison. The choice of B is reinforced. Similar training is conducted with BC and CD. If a class has been established, all of the stimuli have become interrelated. Thus, many new stimulus-stimulus relations are formed. The terms in each such relation will be identified as being related by a subject even though they have never been This research was supported partly by NICHHD Grant presented together previously (Fields & VerRO1-HD21110-01A2, as well as PSC/CUNY Grants have, 1987; Sidman & Tailby, 1982). Each of 666199 and 668457. We thank Kathleen McKay for her expert assistance in the collection and analysis of the data these emergent two-term relations is reprepresented herein. Reprints can be obtained from Lanny sented by one of the lines beneath the letters Fields at the College of Staten Island/CUNY, 130 Stuy- in Figure 1. There are four types of emergent vesant Place, Staten Island, New York, 10301, or from relations: reflexive (AA, BB, CC, DD), symThom Verhave at Queens College/CUNY, Department of Psychology, Kissena Boulevard, Flushing, New York, metrical (BA, CB, DC), transitive (AC, BD, AD), and equivalence (DB, CA, DA) (Bush, 11367. 345
LANNY FIELDS et al.
346
Two-Term Relations Type Sa-Co+
Letter-Line Array
A-B B-C C-D A
B
C
--(C)
Nodes
Training Training Training STIMULI IN CLASS
D
-------(B)-----(C)------> (------(B)-----(C)-------
Intervening
A-A B-B C-C D-D
Reflexive Reflexive Reflexive Reflexive
D-C
Symmetrical
C-B B-A
Symmetrical
A-D D-A
Derivative-T Derivative-E
2-node (B and C) 2-node (B and C)
B-D D-B
Derivative-T Derivative-E
1-node (C) 1-node (C)
Symmetrical
1-node (B) Derivative-T A-C .-----1-node (B) C-A Derivative-E Fig. 1. A letter-line array depicting a four-member equivalence class. The stimuli used to form the class are depicted as the letters A-D. All two-term relations used for training are depicted as arrows above the letters. The letter beneath the tail of the arrow indicates the sample, and the letter beneath the head of the arrow indicates the comparison. All emergent relations are depicted as arrows beneath the letters. Each arrow depicts a separate two-term relation. The letter designation of each two-term relation is listed to the right of the arrow. For emergent relations, the type of relation and the number of intervening nodes found in each derivative relation are also indicated. Derivative-T is a transitive relation. Derivative-E is an equivalence relation.
-------(B)------>
JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR
NUMBER 3
(MAY)
THE EFFECTS OF NODALITY ON THE FORMATION OF EQUIVALENCE CLASSES LANNY FIELDS, BARBARA J. ADAMS, THOM VERHAVE, AND SANDRA NEWMAN THE COLLEGE OF STATEN ISLAND/CUNY AND QUEENS COLLEGE/CUNY A four-member equivalence class (A - B - C - D) can be formed by training AB, BC, and CD. The nodal stimuli, B and C, mediate all of the derivative (transitive and equivalence) relations in the class. The derivative relations AC, CA, BD, and DB are separated by one node, whereas AD and DA are separated by two nodes. How do the number of nodes that separate the stimuli in a derivative relation influence the induction of stimulus control exerted by that relation? Seven college students learned two four-member classes made up of nonsense syllables. After training, all derivative relations were presented repeatedly without informative feedback. Stimulus control exerted by each derivative relation was assessed concurrently. For the 7 subjects, control exerted by the derivative relations increased gradually with repeated presentations. With 6 of the 7 subjects, the one-node relations exerted more control than the two-node relations during the process. However, the disparity between the one- and two-node relations decreased with repeated presentations. Eventually, all derivative relations exerted complete control. The control exerted by derivative relations during induction was inversely related to the number of nodes separating the terms in the derivative relations. These results demonstrate that nodal distance is a determinant of the relatedness of stimuli in equivalence classes. The findings are discussed in terms of remote association, semantic memory networks, and the study of transitive inference. Key words: equivalence class, intervening nodes, derivative relations, remote associations, semantic memory networks, associative distance, nonsense syllables, computer keyboard input, college students
An equivalence class consists of a group of stimuli, all of which become interrelated even though they do not necessarily share any common physical properties (Sidman, 1971). An example of such a class drawn from the realm of organic chemistry consists of the four representations of ethanol: C2H5OH, grain alcohol, liquor, and ethanol. To create a class from a group of N such disparate stimuli, (N - 1) stimulus-stimulus relations must be established by training, with the proviso that each stimulus is used in at least one of the stimulus-stimulus relations (Fields, Verhave, & Fath, 1984). In addition, two different stimuli must be used in each training relation. If the four stimuli in the group are identified
by the letters A, B, C, and D, one way to establish the class is to train the two-term relations AB, BC, and CD, each of which is represented by one of the arrows above the stimulus letters in Figure 1. Each two-term relation is established on a trial-by-trial basis using the conditional discrimination paradigm. For example, during AB training, A is presented as a sample with B as a positive comparison and an unrelated new stimulus (X) as a negative comparison. The choice of B is reinforced. Similar training is conducted with BC and CD. If a class has been established, all of the stimuli have become interrelated. Thus, many new stimulus-stimulus relations are formed. The terms in each such relation will be identified as being related by a subject even though they have never been This research was supported partly by NICHHD Grant presented together previously (Fields & VerRO1-HD21110-01A2, as well as PSC/CUNY Grants have, 1987; Sidman & Tailby, 1982). Each of 666199 and 668457. We thank Kathleen McKay for her expert assistance in the collection and analysis of the data these emergent two-term relations is reprepresented herein. Reprints can be obtained from Lanny sented by one of the lines beneath the letters Fields at the College of Staten Island/CUNY, 130 Stuy- in Figure 1. There are four types of emergent vesant Place, Staten Island, New York, 10301, or from relations: reflexive (AA, BB, CC, DD), symThom Verhave at Queens College/CUNY, Department of Psychology, Kissena Boulevard, Flushing, New York, metrical (BA, CB, DC), transitive (AC, BD, AD), and equivalence (DB, CA, DA) (Bush, 11367. 345
LANNY FIELDS et al.
346
Two-Term Relations Type Sa-Co+
Letter-Line Array
A-B B-C C-D A
B
C
--(C)
Nodes
Training Training Training STIMULI IN CLASS
D
-------(B)-----(C)------> (------(B)-----(C)-------
Intervening
A-A B-B C-C D-D
Reflexive Reflexive Reflexive Reflexive
D-C
Symmetrical
C-B B-A
Symmetrical
A-D D-A
Derivative-T Derivative-E
2-node (B and C) 2-node (B and C)
B-D D-B
Derivative-T Derivative-E
1-node (C) 1-node (C)
Symmetrical
1-node (B) Derivative-T A-C .-----1-node (B) C-A Derivative-E Fig. 1. A letter-line array depicting a four-member equivalence class. The stimuli used to form the class are depicted as the letters A-D. All two-term relations used for training are depicted as arrows above the letters. The letter beneath the tail of the arrow indicates the sample, and the letter beneath the head of the arrow indicates the comparison. All emergent relations are depicted as arrows beneath the letters. Each arrow depicts a separate two-term relation. The letter designation of each two-term relation is listed to the right of the arrow. For emergent relations, the type of relation and the number of intervening nodes found in each derivative relation are also indicated. Derivative-T is a transitive relation. Derivative-E is an equivalence relation.
-------(B)------>
