Transitivity is a key concept in stimulus equivalence and serves as a critical test for establishing stimulus-stimulus relations. It occurs when an untrained relationship between two stimuli emerges as a result of training on other stimulus-stimulus relations. In essence, if a person learns that A = B and B = C, they can derive that A = C without direct training.
Example
A child is taught that the word “dog” (stimulus A) is equivalent to a picture of a dog (stimulus B), and that the picture of the dog (stimulus B) is equivalent to the sound of barking (stimulus C). Without direct training, the child can now associate the word “dog” (stimulus A) with the sound of barking (stimulus C), demonstrating transitivity.