Quantitative and methodological aspects of stimulus equivalence

The number of different ways of linking stimuli in the training phase of a conditional discrimination procedure designed to teach equivalence relations has hitherto been underestimated. An algorithm from graph theory that produces the correct number of such different ways is given. The establishment of equivalence relations requires transitive stimulus control. A misconception in a previous analysis of the conditions necessary for demonstrating transitive stimulus control is indicated. This misconception concerns responding in an unreinforced test trial to a negative rather than a positive comparison stimulus. Such behavior cannot be attributed to discriminative control by degree of association with reinforcement if the negative comparison stimulus has been less associated with reinforcement than the positive comparison stimulus in an antecedent training phase.