Emergent Identity Matching after Successive Matching Training II: Reflexivity or Transitivity?

This is the second of two articles examining the origin(s) of an apparent reflexivity effect in pigeons reported by Sweeney and Urcuioli (2010). Reflexivity refers to an untrained ability to match individual stimuli to themselves after explicit training on conditional relations of the form A–B and B–C, where the first letter of each pair designates the sample stimuli of the trained relations and the second letter of each pair designates the comparison stimuli of those relations. If the conditional relations are also equivalence relations, then a new set of relations should emerge from training (Sidman & Tailby, 1982; see also Sidman, 1990). Specifically, subjects should now do the reverse of what they explicitly learned by matching B samples to A comparisons (B–A matching) and C samples to B comparisons (C–B matching), a phenomenon known as symmetry (a.k.a. associative symmetry—Frank & Wasserman, 2005; Lionello-Denolf, 2009; Sidman, Rauzin, Lazar, Cunningham, Tailby, & Carrigan, 1982; Urcuioli, 2008). In addition, they should now match the A samples to the C comparisons (A–C matching)— transitivity (e.g., D'Amato, Salmon, Loukas, & Tomie, 1985; Kuno, Kitadate, & Iwamoto, 1994; Lipkens, Kop, & Matthijs, 1988). Finally, they should match each stimulus to itself (e.g., A samples to A comparisons)—reflexivity (Sidman & Tailby, 1982). To test for reflexivity and to evaluate the stimulus-class mechanism proposed by Urcuioli (2008) for this and other emergent effects in pigeons, Sweeney and Urcuioli (2010) concurrently trained pigeons on three successive (go/no-go) matching tasks (cf. Wasserman, 1976). Two were symmetrically reinforced (i.e., “mirror-image”) arbitrary matching tasks (A–B and B–A); the third was identity matching involving one set of stimuli appearing in arbitrary matching (B–B). Later, pigeons received periodic, nonreinforced probe trials in which the A samples from the A–B task were followed by the A comparisons from the B–A task. For 5 of the 6 pigeons, comparison response rates were higher on probe trials in which the A comparison matched the preceding A sample (e.g., red comparison after a red sample) than on probe trials in which the A comparison did not match the preceding A sample (e.g., red comparison after a green sample). In short, the three sets of baseline relations yielded emergent A–A matching, a finding consistent with Urcuioli's (2008) theoretical prediction (see below) and interpreted by Sweeney and Urcuioli (2010) as an example of reflexivity. Readers will undoubtedly notice that the conditional relations used in training by Sweeney and Urcuioli (2010)—A–B, B–A, and B–B matching—differ in a number of ways from the supposedly sufficient A–B and B–C baseline relations mentioned earlier. First, the two arbitrary matching tasks involved exactly the same nominal stimuli, albeit with their roles as samples and comparison reversed from one task to another. Second, including B–B identity matching meant that training involved three rather than two sets of conditional relations. The reason for these differences was entirely theoretical. Specifically, using the same assumptions that Urcuioli (2008) did to account for associative symmetry (Frank & Wasserman, 2005; Urcuioli, 2008, Experiment 3), it was possible to predict the successive matching training contingencies that should yield reflexivity. Those assumptions are that (1) the functional stimuli in successive matching are the nominal stimuli plus their ordinal position within a matching trial (viz., first or second, depending on whether a stimulus appears as a sample or a comparison, respectively); (2) the reinforcement contingencies for successive matching (e.g., Wasserman, 1976) promote the development of stimulus classes containing the elements of the reinforced sample–comparison combinations; and (3) elements common to more than one class cause their respective classes to merge. To illustrate, if a red (R) sample → triangle (T) comparison combination is reinforced in A–B matching, a triangle sample → red comparison combination is reinforced in B–A matching, and a triangle sample → triangle comparison combination is reinforced in B–B matching, the theory anticipates the development of the following three stimulus classes: [R1, T2], [T1, R2], and [T1, T2]. In this notation, the number after each letter designates the ordinal position of each matching stimulus (viz., as a sample or comparison)1. Note, too, that some classes have an element in common—viz., the [R1, T2] and [T1, T2] classes share T2 (the triangle comparison) and, likewise, the [T1, R2] and [T1, T2] classes share T1 (the triangle sample). If common elements cause their respective classes to merge (Urcuioli, 2008; see also Mackay, Wilkinson, Farrell, & Serna, 2011), the net result should be a [R1, R2, T1, T2] class. This four-member class consists of elements comprising each explicitly reinforced baseline relation (e.g., R1 and T2 of the red sample → triangle comparison relation). In addition, it has the elements of the untrained red sample → red comparison (R1–R2) relation. A person familiar with stimulus equivalence and who observed pigeons in testing respond more to a hue comparison (e.g., R2) when it matched its preceding hue sample (e.g., R1) than when it did not would likely describe this response-rate difference as reflexivity. Despite appearances, however, this emergent effect is not strictly reflexivity by Urcuioli's (2008) account because “matching each stimulus to itself” entails matching red to red (a R–R relation) and green to green (a G–G relation) and, theoretically speaking, R1–R1 and G1–G1 relations cannot be tested because “1” cannot be used to designate the second stimulus in a sequence. The definition of reflexivity treats the functional and nominal matching stimuli as the same. By contrast, Urcuioli's (2008) theory states that functional matching stimuli in pigeons' successive matching are compounds consisting of a nominal stimulus (e.g., red or green) and its ordinal position in a trial (first or second). Thus, a red comparison (R2), is a different stimulus than a red sample (R1), so matching the former to the latter is not “matching each stimulus to itself.” These distinctions should not, in our view, detract from the finding that certain sets of successive matching contingencies yield novel, untrained behavior not previously observed in nonhuman animals (Frank & Wasserman, 2005; Sweeney & Urcuioli, 2010; Urcuioli, 2008, Experiment 3). Urcuioli's (2008) theory contributes to these noteworthy empirical findings by proposing mechanisms to explain why those contingencies yield such observed emergent effects. That said, the present article considers the possibility that higher comparison response rates on matching than on nonmatching A–A probe trials following the aforementioned baseline contingencies (Sweeney & Urcuioli, 2010) could arise for reasons other than those specified by Urcuioli (2008). The three experiments described here continue along the lines of Urcuioli (2011) who asked whether such emergent performances might represent generalization of identity matching from the explicitly trained B–B baseline relations to the untrained A–A relations of testing. To evaluate this alternative account, Urcuioli (2011) trained pigeons on symmetrically reinforced arbitrary matching tasks (A–B and B–A) plus an identity matching task with stimuli not appearing in arbitrary matching (viz., C–C). If the explicitly reinforced C–C identity relations generalize to other stimuli, A–A matching should emerge in testing. On the other hand, Urcuioli's (2008) theory clearly predicts that such training should not yield emergent A–A matching. Contrary to theoretical prediction but consistent with generalized identity (Oden, Thompson, & Premack, 1988; Pena, Pitts, & Galizio, 2006), some pigeons did show an emergent A–A effect. There is, however, another explanation which could potentially account for these results and those of Sweeney and Urcuioli (2010)—namely, transitivity. After all, pigeons trained on A–B, B–A, and B–B successive matching (Sweeney & Urcuioli, 2010; Urcuioli, 2011) versus A–B, B–A, and C–C successive matching (Urcuioli, 2011) share two potentially consequential baseline relations: A–B and B–A. If the functional matching stimuli in these tasks do not have an ordinal-position component (as assumed by Urcuioli, 2008) and if these baseline relations are transitive (cf. Lipkens et al., 1988; Strasser, Ehrlinger, & Bingman, 2004), then A–A matching should emerge in testing. Colloquially speaking, if A means B and B means A, then A means A (Vasconcelos, 2008). To take a specific example, if comparison responding on red–triangle and triangle–red combinations are both reinforced in training, then pigeons should preferentially respond to red after red (red–red) in testing if the reinforced baseline relations are transitive. By contrast, Urcuioli's (2008) theory predicts that A–B and B–A training alone are insufficient to produce that effect precisely because of the assumption regarding the ordinal-position component of the functional matching stimuli. Using a specific illustrative example, if reinforced red sample–triangle comparison (R1–T2) trials and reinforced triangle sample–red comparison (T1–R2) trials are components of A–B and B–A arbitrary matching, respectively, these combinations have no functional elements in common. Stated otherwise, R1 ≠ R2 and T1 ≠ T2, so each must be regarded as a different stimulus. Consequently, a class merger in which R1 and R2 join the same stimulus class—the theoretical basis for an emergent A–A effect—cannot occur. The present experiments contrast the theoretical prediction of no emergent A–A matching following such training with a transitivity account of the reflexivity results reported by Sweeney and Urcuioli (2010) and the generalized identity findings of Urcuioli (2011).