Axiom 5


[Hughes and Cresswell, 1996]

Axiom 5


It is the defining axiom of the system S5

This axiom is also called axiom "E" by Hughes and Cresswell. This leads to confusion when dealing with the "E" modal logic systems, and when dealing with the propositional logic system E, so I've chosen to follow the naming conventions of Chellas and call it axiom 5. The strict form of this axiom is called M10 by Zeman.


S5 = Axiom K: L(p>q) > (Lp>Lq) + Lp>p + Axiom 5 [Mp>LMp] [Hughes and Cresswell, 1996, p58]

S9 = S3 + Axiom 5 [Mp>LMp] + MMp [Axiom S] [Hughes and Cresswell, 1996, p364]

S3.5 = S3 + Axiom 5 [Mp>LMp] [Hughes and Cresswell, 1996, p364]

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