and when they combine this model and the original models, they get the following: O A

a single model, with the implicit (ellipsis) model eliminated. The implicit model can be removed because all the other models it implicitly indicates are ones in which there is not a circle.

To form a conclusion this model is described in a parsimonious fashion with the sentence: "there is a triangle". This is how the model theory accounts for the valid, modus ponens inference. This inference can be made readily from the initial representation of the conditional, without any need to make the implicit information explicit. In the more difficult modus tollens inference, subjects are given the extra premise "There is not a triangle" represented by the model:

To combine this model with the initial models:

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