Symmetry is one of three derived relations (along with transitivity and reflexivity) that indicate that explicitly trained conditional relations are equivalence relations and that the elements of those trained relations are members of a stimulus class. Although BA symmetry is typically observed after AB conditional discrimination training in humans, it has been an elusive phenomenon in other animals until just recently. This paper describes past unsuccessful attempts to observe symmetry in non-human animals and the likely reasons for that lack of success. I then describe how methodological changes made in response to the earlier findings have now yielded robust evidence for symmetry in pigeons, and what these changes indicate about the functional matching stimuli. Finally, I describe a theory of stimulus-class formation (Urcuioli, 2008) which specifies how and why symmetry and other derived relations arise from different sets of trained relations. These derived relations are noteworthy because they demonstrate an impressive repertoire of non-similarity-based categorization effects in animals and the generative effects of reinforcement and stimulus control processes on behavior.
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