Human reasoning violates all normal modal logics
Marco Ragni and Phil Johnson-Laird have a new paper in CogSci 2018 that shows how human reasoning violates all orthodox systems of modal logic. You can read the paper here.
The abstract is:
Reasoning about possibilities is fundamental in daily life and in artificial intelligence. It is formalized in modal logics, of which there are infinitely many. Two experiments showed that individuals make inferences that are parsimonious about possibilities, and that they reject conclusions referring to possibilities that the premises do not support. Both sorts of inference contravene modal logics, i.e., the simplest system of modal logic and the infinite number of systems based on it.