Interactive Parallel Models: No Virginia, Violation of Miller's Race Inequality does not Imply Coactivation and Yes Virginia, Context Invariance is Testable

One vein of our research on psychological systems has focused on parallel processing models in disjunctive (OR) and conjunctive (AND) stopping-rule designs. One branch of that research has emphasized that a common strategy of inference in the OR situations is logically flawed. That strategy equates a violation of the popular Miller race bound with a coactive parallel system. Pointedly, Townsend & Nozawa (1997) revealed that even processing systems associated with extreme limited capacity are capable of violating that bound. With regard to the present investigation, previous theoretical work has proven that interactive parallel models with separate decision criteria on each channel can readily evoke capacity sufficiently super to violate that bound (e.~g., Colonius & Townsend, 1997; Townsend & Nozawa, 1995; Townsend & Wenger, 2004). In addition, we have supplemented the usual OR task with an AND task to seek greater testability of architectural, decisional, and capacity mechanisms (e.~g., Eidels et al., 2011; Eidels et al., 2015). The present study presents a broad meta-theoretical structure within which the past and new theoretical results are embedded. We further exploit the broad class of stochastic linear systems and discover that interesting classical results from Colonius (1990) can be given an elegant process interpretation within that class. In addition, we learn that conjoining OR with AND data affords an experimental test of the crucial assumption of context invariance, long thought to be untestable.