gi1(x) = g12(x)
for all x and for i = 1, 2, 3, and 4.
Let x12 be the criterion between the representations of A1 and A2. Because decisional separability holds and responding is context-free, the similarity of stimulus A1Bj to stimulus A2Bj is found from Equation 7 to be
In a similar fashion, it can be shown that s(A3B1, A4B1) = s(A3B2, A4B2). Without loss of generality, assume s(A3B1, A4B1) > s(A1B1, A2B1). If the function relating similarity and dissimilarity is monotonically decreasing, then
d(A1B1, A2B1) > d(A3B1, A4B1) iff d(A1B2, A2B2) > d(A3B2, A4B2).
Therefore, consistency holds.
This research was supported in part by a National Science Foundation Grant BNS88-19403 to F. Gregory Ashby and a Social Science-Humanities Grant to W. Todd Maddox. I especially wish to thank Greg Ashby for help at all stages of this research. I would also like to thank Helena Kadlec, Rich Ivry, Jack Loomis, and John Cotton for helpful comments on an earlier version of this manuscript and Bill Lee, Jerry Balakrishnan, and Geoff Boynton for many helpful discussions.
Correspondence concerning this article should be addressed to W. Todd Maddox, Department of Psychology, University of California, Santa Barbara, CA 93106.