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The McKinsey axiom is not canonical. (English) Zbl 0744.03019

Let \(L\) be a logic, and \({\mathcal F}_ L\) a canonical frame which invalidates every nontheorem of \(L\). If, in addition, each \(L\)-theorem is valid in \({\mathcal F}_ L\), then \(L\) is said to be canonical. The logic \(KM\) is the smallest normal modal logic that includes the McKinsey axiom \(\square\diamondsuit\varphi\to\diamondsuit\square\varphi\). The paper contains the proof that this axiom is not valid in the canonical frame for \(KM\).

MSC:

03B45 Modal logic (including the logic of norms)
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