The classical logic operators (e.g., "and", "or", "if_then", "if and only if") play a fundamental role in concept formation, syntactic construction, semantic expression and in deductive reasoning. In spite of this very general and basic role, there are relatively few comprehensive studies in the literature that focus on their conceptual nature. Bourne (1970) studied and observed the learning difficulty ordering of a small subset of six out of the 16 modal concept structures that characterize the logic operators semantically. His method was significantly different from more traditional methods of studying concept learning difficult in terms of classification behavior and he was not able to provide a satisfactory explanation for the results of his study. We remedied these deficits by, for the first time, examining experimentally and theoretically all 16 of these atomic concepts using acoustic and visual categorical stimuli and a more traditional classification paradigm (Vigo, Barcus, Doan, and Pinegar, 2015). Remarkably, results for the acoustic and visual stimuli were nearly identical, corroborating the fundamental importance of these modal concepts to the human cognitive system. We compare Bourne's original results to our results and show that the Generalized Invariance Structure Theory Model (GISTM; Vigo, 2013, 2014), without free parameters, better accounts for classification error rates and reaction times (with respect to both visual and acoustic stimuli) than the Generalized Context Model (GCM; Nosofsky, 1984, 1986), the Minimization Complexity Model (MinC; Vigo, 2006) and the Minimal Description Model (MinD; Feldman, 2000). Finally, we explore the connection between our results and those in Vigo (2009) where the logic operators are interpreted by Modal Similarity Theory (MST) as degrees of similarity to the "if and only if" operator.
School of Informatics and Computing, Indiana University.