Notre Dame Journal of Formal Logic

A Basic System of Congruential-to-Monotone Bimodal Logic and Two of Its Extensions

I. L. Humberstone


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.

Article information

Notre Dame J. Formal Logic, Volume 37, Number 4 (1996), 602-612.

First available in Project Euclid: 16 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}


Humberstone, I. L. A Basic System of Congruential-to-Monotone Bimodal Logic and Two of Its Extensions. Notre Dame J. Formal Logic 37 (1996), no. 4, 602--612. doi:10.1305/ndjfl/1040046144.

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