Re: Modal logic Nessitation rule

translogi wrote:

Am I getting confused?

I seem to have lost grips with the nessitation rule

Does it only apply to Theorems/ axioms (valid in all worlds) or also
to premmisses (valid in some worlds)?

The rule says that if A is a theorem, then LA is a theorem also.
This is _invalid_:

1 A assumption
2 LA from 1 by nessitation
3 A -> LA from 1 and 2 by conditional proof
discharging assumption 1

If it is only the first what is the fuzz al about?
But also then how aboul modal logics where the rule doesn't hold.
(like Grz)

Lots of logics don't have it, such as the classical and non-normal
families. For the former there is a book by Brian Chellas.

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