Does the law of excluded middle (p or -p is provable) hold in modal logic?

I would personally say yes, for from an algebraic logic point of view, modal logic is modelled via e.g. closure algebras (which are Boolean algebras), and the join of p and -p equals the unit in every Boolean algebra. But, I would like a confirmation (or refutation) from a logician/philosopher. Thanks in advance.

1 Answer 1


Given that p or ¬p is a classical tautology, and normal modal logic has all tautologies as theorems and the necessitation rule, then □(p or ¬p) is a theorem, so yes. Having said that, modal logic refers to a whole family of logics, rather than a single logic, so it is perfectly possible to set up a logic in which this doesn't hold, such as constructive modal CS4.


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