Important characteristics of transitivity:
A young hearing disabled 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 an American Sign Language (ASL) card (e.g., an illustration of someone signing "radio") 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 ASL card. 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.
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 says the name of an object (e.g., "radio"); then, he places the three word cards on the table and tells Lois to choose the one that goes with it (e.g., "correct" choice would be the printed word radio). 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 transitivity. Lois was taught an AB relation, A being the spoken word (e.g., "radio") and B being the picture (e.g., radio illustration). Lois was also taught a DC relation, D being the ASL sign (e.g., an illustration of someone signing "radio") and C being the printed word (e.g., radio). These two trained relations do not share a common element. (Given that pictures of objects and their corresponding ASL signs have already been related through some other training, transitivity may be involved in accounting for Lois' test performance, but in an indirect way.)
The second item is an example of transitivity. As noted above, Lois was taught an AB relation, A being the spoken word (e.g., "radio") and B being the picture (e.g., radio illustration). She was also taught a BC relation, B being the picture (e.g., radio illustration) and C being the printed word (e.g., radio). On the test, Lois reliably matched the comparison stimulus from the second trained relation (e.g., radio) to the sample stimulus from the first trained relation (e.g., "radio"), an AC relation. Because she was able to do this without training, the AC relation is considered to have emerged as a consequence of learning the AB and BC relations.