The Modal Square of Opposition and the Mental Models Theory

The mental models theory is a current approach trying to account for human thought and hence communication by highlighting the action of semantics and ignoring, to a large extent, syntax. However, it has been argued that the theory actually contains an underlying syntax related to any kind of modal logic. This paper delves into this last idea and is intended to show that the concepts of possibility and necessity as understood in it fulfill the basic requirement that, according to Fitting and Mendelsohn, every modal logic has to meet: to satisfy the relationships provided by the Aristotelian modal square of opposition.