Rectifying the Mischaracterization of Logic by Mental Model Theorists

Khemlani et al. (2018) mischaracterize logic in the course of seeking to show that mental model theory (MMT) can accommodate a form of inference ( $$ , let us label it) they find in a high percentage of their subjects. We reveal their mischaracterization and, in so doing, lay a landscape for future modeling by cognitive scientists who may wonder whether human reasoning is consistent with, or perhaps even capturable by, reasoning in a logic or family thereof. Along the way, we note that the properties touted by Khemlani et al. as innovative aspects of MMT-based modeling (e.g., nonmonotonicity) have for decades been, in logic, acknowledged and rigorously specified by families of (implemented) logics. Khemlani et al. (2018) further declare that $$ is "invalid in any modal logic." We demonstrate this to be false by our introduction (Appendix A) of a new propositional modal logic (within a family of such logics) in which $$ is provably valid, and by the implementation of this logic. A second appendix, B, partially answers the two-part question, "What is a formal logic, and what is it for one to capture empirical phenomena?"