## A

In this notation, each line represents a new model. These three models represent all those situations where the premise is true, but not the situation when the premise is false (compare it to the truth table in Table 16.1). The "-" symbol is a propositional tag in the model, used to indicate "not". Intuitively, this means that when people understand the premise—"if there is a circle then there is a triangle"—they represent it by states of affairs described by this sentence; namely, a situation where there is a circle and a triangle, a situation where there is not a circle and there is a triangle, and a situation where there is neither a circle nor a triangle.

However, people attempt to represent as little information as possible because of their processing limitations and so they build representations that indicate the various alternative situations implicitly. So, Johnson-Laird and Byrne suggest that when people understand this premise they build the following initial models:

This representation contains just two models, one representing a situation where there is a circle and a triangle and one (indicated by the three dots or ellipsis) indicating that there are other alternative models (i.e., the two other explicit models shown earlier). These explicit models can be added or "fleshed out" later. The square brackets around the circle mean that the circle has been represented "exhaustively" in the model; that is, the alternative models will not contain a circle because in any other model where a circle occurs, there has to be a triangle (see Johnson-Laird & Savary, 1996, for a notational variant called footnotes). When reasoners are given a second premise— "There is a circle"—they construct a model in which there is just a circle: