A basic system of congruential-to-monotone bimodal logic and two of its extensions.

*(English)*Zbl 0883.03010Summary: If what is known need not be closed under logical consequence, then a distinction arises between something’s being known to be the case (by a specific agent) and its following from something known (to that subject). When each of these notions is represented by a sentence operator, we get a bimodal logic in which to explore the relations between the two notions.

##### MSC:

03B45 | Modal logic (including the logic of norms) |

03A05 | Philosophical and critical aspects of logic and foundations |

##### Keywords:

epistemic logic; epistemically necessary; epistemically possible; failure of closure of knowledge under logical consequence; bimodal logic
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\textit{I. L. Humberstone}, Notre Dame J. Formal Logic 37, No. 4, 602--612 (1996; Zbl 0883.03010)

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