I am new to modal logics and would really appreciate it if someone would be able to help me out with this practice question. I’ve established the validity theorem in T with an axiomatic proof, but I can’t seem to wrap my head around how to derive the same result by constructing a counter model in T, and to show that it does not hold in weaker system.

Any help is much appreciated!

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    Commented Apr 5, 2018 at 0:37

1 Answer 1


There is no counter-model in T, since it is a theorem of T.

As for K, take a model with two worlds α and β where β is possible relative to α, but nothing is possible relative to β. Make P true in β. Then your sentence fails in α.


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