Notre Dame Journal of Formal Logic

Note on Extending Congruential Modal Logics

Lloyd Humberstone

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It is observed that a consistent congruential modal logic is not guaranteed to have a consistent extension in which the Box operator becomes a truth-functional connective for one of the four one-place (two-valued) truth functions.

Article information

Notre Dame J. Formal Logic, Volume 57, Number 1 (2016), 95-103.

Received: 27 July 2013
Accepted: 4 October 2013
First available in Project Euclid: 30 September 2015

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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}

modal logic Post completeness congruential modal logics neighborhood semantics


Humberstone, Lloyd. Note on Extending Congruential Modal Logics. Notre Dame J. Formal Logic 57 (2016), no. 1, 95--103. doi:10.1215/00294527-3315588.

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