@Kleinmk5,
One of the tasks of psychology is to
account for 'logical thinking'. Piaget was one who understood this and although some of his findings are disputed, his metalogical 'genetic epistemology' was a major breakthrough in the study of cognition. This transcendence of traditional logic is also a feature of the 'embodiment theoreists' who reject the traditional logic of computers as a valid model for cognitive behavior. (ref: Merleau-Ponty, Rosch et al).
And as regards 'probabilistic thinking', the concept of 'fuzzy ssts' (Kosko) provides a useful introduction to the dynamic fluidity of set membership.