A classic semantic makes it possible to characterize the notion of truth/falsity for sentences of a first order language $ \mathcal L_1 ^ {=} $. Explain importance of ensuring that $ \mathcal L_1 ^ {=} $ - closed formula $ \alpha $ is true in a structure. The formula $ \alpha $ has the following the syntactic form: $ (\exists x\lnot Rx \mathbf a \to \forall xK \mathbf ax) $, where R, K, and $ \mathbf a $ are respectively symbols of predicates (binary) and individual constant.
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I'm not sure how to proceed. What exactly does the exercise want?
A formula to be closed means that the formula does not have free variables. And why would a closed formula be more important than an open formula in a structure?