Important characteristics of symmetry:
A young child, Lois, is learning how to read. On some learning trials, her teacher first says the name of an object (e.g., "radio"), and then he lays three picture cards on the table. Lois is told to choose the picture (e.g., radio illustration) that goes with the spoken word. On other learning trials, her teacher first shows her one of the picture cards and then he puts three word cards on the table. Lois is told to choose the printed word (e.g., radio) that goes with the picture. All correct responses on these learning trials are praised by her teacher. Later, after the first two tasks are mastered, Lois is tested on another task. Her teacher first shows her one of the picture cards (e.g., radio illustration); then, he asks her to say the word that goes with it (e.g., "correct" response would be saying "radio"). Lois performs perfectly on this third task, even though her teacher did not prompt or praise her correct answers.
A young child, Lois, is learning how to read. On some learning trials, her teacher first says the name of an object (e.g., "radio"), and then he lays three picture cards on the table. Lois is told to choose the picture (e.g., radio illustration) that goes with the spoken word. On other learning trials, her teacher first shows her one of the picture cards and then he puts three word cards on the table. Lois is told to choose the printed word (e.g., radio) that goes with the picture. All correct responses on these learning trials are praised by her teacher. Later, after the first two tasks are mastered, Lois is tested on another task. Her teacher first shows her one of the word cards (e.g., radio); then, he places the three picture cards on the table and tells Lois to choose the one that goes with it (e.g., "correct" choice would be the radio illustration). Lois performs perfectly on this third task, even though her teacher did not prompt or praise her correct answers.
The first item is not an example of symmetry. Lois was taught two things: (1) an AB relation, A being the spoken word (e.g., "radio") and B being the picture (e.g., radio illustration); and (2) a BC relation, B being the picture (e.g., radio illustration) and C being the printed word (e.g., radio). Also, her "correct" responses on the third task were not reinforced, and thus this test was assessing emergent behavior. We could even say that the test did, in a sense, involve a reversal of the second task, if one views the BC relation as spoken name / picture and the test as picture / spoken name. However, the test was not conducted in a match-to-sample paradigm. If it was, Lois would have been asked to select the auditory stimulus that goes with the picture. Subjects in equivalence research are frequently able say the names like Lois did, but this is not a direct assessment for symmetry of a relation trained in the match-to-sample paradigm (Sidman & Tailby, 1982; see also Sidman, 1994, pp. 227-228, p. 363). (It has been suggested, however, that stimulus equivalence is possible outside the restrictions imposed by match-to-sample paradigm, provided that the response mode is the same for both the trained and tested relations: Hall & Chase, 1991.)
The second item is an example of symmetry. As noted above, Lois was taught a BC relation, B being the picture (e.g., radio illustration) and C being the printed word (e.g., radio). In other words, she learned to match the printed word to the picture. On the test, she performed perfectly in accordance with the reversal of this task, that is, she matched the picture to the printed word, a CB relation. Because she was able to do this without training, the CB relation is considered to have emerged as a consequence of learning the BC relation.