Geodesic
An Observation Concerning Porte’s Rule in Modal Logic
Bulletin of the Section of Logic, Tome 44 (2015) no. 1-2.

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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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     author = {French, Rohan and Humberstone, Lloyd},
     title = {An {Observation} {Concerning} {Porte{\textquoteright}s} {Rule} in {Modal} {Logic}},
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French, Rohan; Humberstone, Lloyd. An Observation Concerning Porte’s Rule in Modal Logic. Bulletin of the Section of Logic, Tome 44 (2015) no. 1-2. http://geodesic.mathdoc.fr/item/BSL_2015_44_1-2_a1/