An observation concerning porte's rule in modal logic

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Bulletin of the Section of Logic 44 (1/2):25-31 (2015)
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Abstract

It is well known that no consistent normal modal logic contains (as theorems) both ♦A and ♦¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent normal modal logic contains ♦A, or else no consistent normal modal logic contains ♦¬A.

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10.18778/0138-0680.44.1.2.04

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Author Profiles

Rohan French
University of California, Davis
Lloyd Humberstone
Monash University

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References found in this work

Some embedding theorems for modal logic.David Makinson - 1971 - Notre Dame Journal of Formal Logic 12 (2):252-254.
Post completeness in modal logic.Krister Segerberg - 1972 - Journal of Symbolic Logic 37 (4):711-715.
The Power of a Propositional Constant.Robert Goldblatt & Tomasz Kowalski - 2014 - Journal of Philosophical Logic 43 (1):133-152.
Necessity and Relative Contingency.Claudio Pizzi - 2007 - Studia Logica 85 (3):395-410.

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