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I talk about relational Frames a lot here, so figured I should review again. It's based on the concept of a verbal operant, and rooted in the 4 term contingency: Something in the environment triggers your response (accounting for your motivation, importantly) which then alters the environment,

changing how you feel, which either reinforces or punishes you - decreasing or increasing future behavior. You're hungry, see food in the fridge, make a sandwich, eat it, feel good, likely will make another next time you're hungry.

The verbal operant describes how verbal communities (e.g. a language or culture) reinforce communication for wants, for labeling things, for listening behavior, etc. After the response to the environment, the individual receives reinforcement (social, artificial, etc.).

What an individual is building up is a repertoire of responding to stimuli. A bird is a "bird". "Fish" is a fish. 2 + 2 is "four". That feeling in my chest is "sadness". e.g. the word cookie has levels of use across operants: I want a cookie, it is a cookie, the cookie is here. You bake a cookie.

But behaviorists noticed something funny happens - generalization. Not only will their repertoire grow, but their ability to independently learn and generalize grows. This is partially accounted for by increased access to reinforcement by an expanded repertoire of verbal behavior,

Usually, it's reflexive or symmetrical. But sometimes transitive, where an untrained relation occurs.

For instance, if initially "ball" is trained for ball, it may be only an exact replica that evokes responding (A=A). But the learner begins to 'loosen' to other types of balls (A=B). Then, if we play with ball outside sometimes (C), the presence of being outside might evoke the word "ball" (A=C)

Which brings us to Relational Frame Theory. When researchers looked more closely at stimulus equivalence, and specifically generalization, they found subtle variables at work. The generalizations seemed to be arbitrarily applicable.