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Prof. Dr. Jürgen Dix · Department of Informatics, TUC <strong>Multiagent</strong> <strong>Systems</strong>, WS 06/07 487/731<br />

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

As in classical logic, one can ask about a<br />

complete axiom system. Is there a calculus that<br />

allows to derive all sentences true in all Kripke<br />

models?<br />

Definition 7.6 (System K)<br />

The system K is an extension of the propositional<br />

calculus by the axiom<br />

Axiom K (□φ ∧ □(φ → ψ)) → □ψ<br />

and the inference rule<br />

ϕ<br />

(Necessitation)<br />

□ϕ .

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