Does the inclusive disjunction really mean the conjunction of possibilities?

There is an ongoing dispute in the psychology of reasoning about how people interpret disjunctions, p or q. In the original mental models theory (MMT1) people interpret p or q as the disjunction of three possibilities (possibly p¬q, or possibly ¬pq, or possibly pq, where "¬" = not). p or q is true if one disjunct is actually true. In a recent revision of mental models theory (MMT2), people interpret p or q as a conjunction of the three possibilities, and they treat it as true only if each is possible and ¬p¬q is impossible. Two experiments investigated possibility and truth judgments about disjunctions given sets consisting of one or more of the four cases (p¬q, ¬pq, pq, and ¬p¬q). The results showed that in both possibility and truth judgments, participants' interpretations of disjunctions were only consistent with MMT1. Inclusive disjunctions imply the disjunction of the three possibilities, and they are true when one of the three cases (p¬q, ¬pq, and pq) is actual. These findings support MMT1, but not MMT2. In conclusion, the revised mental models theory may be unnecessary for disjunctions.

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