New answers tagged modal-logic
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Actually, $p$ has to be a tautology.
For the sake of completeness, let's consider an example about how it can be used in a proof.
Assume the following axioms and inference rules:
A1. All tautologies of propositional calculus
A2. $(\square_i \phi \land \square_i (\phi \Rightarrow \psi) \Rightarrow \square_i \psi \hspace{1cm}i=1,\cdots, n$ $\hspace{1cm}$ ...
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The key-phrase here is `Jankov-Fine formulas'. See Theorem 95 and Exercise 98 here: http://www.illc.uva.nl/Research/Reports/PP-2006-25.text.pdf. So, by Theorem 95, if $F$ and $G$ are finite rooted frames which validate the same formulas, each of them is a $p$-morphic image of a generated subframe of the the other. By Exercise 98, this implies that they are ...
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