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Is there any epistemic modal logic in which the knowledge of a conjunction is not implied by the knowledge of its conjuncts, i.e.

$\Box A\wedge\Box B\not\Rightarrow\Box(A\wedge B)?$

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  • $\begingroup$ I don't know if any such logic was studied (very probably yes), but if yes, it might be helpful to be aware that such logic would be a non-normal modal logic. $\endgroup$
    – Luka Mikec
    Jan 12, 2015 at 13:31

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The complexity theoretical aspect of some such logics is investigated in:

The paper also includes a reference to Vardi's '86 paper which apparently contains more on such logics (I have not read that one, though).

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