ABSTRACT
We describe an algorithm that constructs mental models of assertions containing sentential connectives, such as and, if, and or. It performs at three levels of expertise depending on the completeness of the models it constructs. At a rudimentary level of performance, it constructs models that make explicit as little as possible. One unexpected consequence is that it produces the same explicit models for assertions of the form:
if p then q, and if r then s
if p then q, or if r then s
p and q, or r and s.
We initially suspected that there was a bug in the algorithm (or theory), but there was not. We therefore carried out two experiments with logically-untrained subjects. Their results confirmed the phenomena: for many individuals, a conjunction of conditionals is equivalent to their disjunction, which in turn is equivalent to a disjunction of conjunctions.
