Meaningful boundaries create boundary conditions for control

A similar assumption (that the boundary needs to be meaningful) could be inferred from a prior study that looked at transfer beyond a different type of reference frame using a prime-probe task. Kunde et al. (2003) found that compatibility effects (reflecting compatibility of responses corresponding to a prime number and a to-be-judged probe number) were found for a prime-only set (e.g., 2, 3, 7, and 8) that never appeared as targets when the target set included a larger range (e.g., 1, 4, 6, and 9) that “encompassed” numbers within the prime-only set. However, and most importantly for present purposes, when the target set (e.g., 3, 4, 6, and 7) had a smaller range such that the numbers from the prime-only set fell outside of that range (e.g., 1, 2, 8, and 9), compatibility effects were not observed. That is, transfer did not extend beyond the reference frame. The reference frame was arguably meaningful in that participants’ knowledge of a mental number line, for example, distinguished numbers in and outside the frame.

As a reviewer pointed out, the reduction in the CSPC effect in Experiment 3b was driven primarily by faster RTs to congruent trials in both MC and MI locations in Experiment 3a compared to 3b. The faster RT for congruent trials in the MC location in 3a compared to 3b is consistent with the interpretation that participants in 3a learned a relaxed control state for the MC location resulting in greater processing of the flanker arrows (and thus greater facilitation in the form of faster RT) compared to 3b (where overall an intermediate, 50% congruent control state was learned). It is surprising that the same speed up was observed for congruent trials in the MI location in Experiment 3a compared to 3b (again indicating greater facilitation from the flankers in 3a) considering that a more focused control state was presumably retrieved in 3a than 3b (where, again, an intermediate control state was learned) resulting in greater filtering of the flankers in 3a. However, it is important to note that theorizing in the CSPC literature has tended to focus on differences in the overall CSPC effect (reflecting differences in compatibility effects between locations) and not differences in select trial types, unlike for example the item-specific proportion congruence (ISPC) literature which has observed fairly consistent patterns of ISPC effects and theorizing exists that anticipates specific patterns of ISPC effects based on differences in select trial types (see, e.g., Bugg & Dey, 2018; Bugg et al., 2011a, 2011b; Suh & Bugg, 2021). Here, the difference in the overall CSPC effect is in the direction consistent with the interpretation that CSPC effects are weaker when a meaningful boundary is present (i.e., in Exp 3b compared to 3a).

We thank an anonymous reviewer for this suggestion.