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Prof. Dr. Jürgen Dix · Department of Informatics, TUC <strong>Multiagent</strong> <strong>Systems</strong>, WS 06/07 492/731<br />

7. Modal Logic 3. Axioms for Modal Logics<br />

Definition 7.9 (Extending K by Axioms D, T, 4,5)<br />

The system K is often extended by (a subset of)<br />

the following axioms:<br />

K (K i φ ∧ K i (φ → ψ)) → K i ψ<br />

D ¬K i (ϕ ∧ ¬ϕ)<br />

T K i ϕ → ϕ<br />

4 K i ϕ → K i K i ϕ<br />

5 ¬K i ϕ → K i ¬K i ϕ<br />

called as above by historical reasons. The system<br />

consisting of KT45 is also called S5.

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