Artificial intelligent assistant

Satisfaction in models of non-sentences? I know the definitions for satisfaction of a sentence in a model but if there are free variables in a formula does that mean that it isn't true or false? (as determined by the model)Thanks

The answer depends on the fine print of the semantic story.

One common line makes it come out that a wff with free variables counts as true-in-$\mathcal{M}$ just when its universal closure comes out true.

But alternatively you can have it that a wff with free variables gets no true-value with respect to $\mathcal{M}\ $ -- it only gets a value with respect to $\mathcal{M} + \mathcal{I}$ where $\mathcal{I}$ is an assignment function mapping variables to elements of $\mathcal{M}$'s domain (in effect giving the variables an interpretation as temporary names).

In some ways, the second story is more natural: the first conforms with informal mathematical practice of treating sentences with free variables as implicitly universally quantified. But you can go either way.

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