Axiom K

Notes

[Hughes and Cresswell, 1996]

[Chellas, 1980]

Axiom

L(p>q)>(Lp>Lq)

This axiom is part of all Normal modal logic systems. [Hughes and Cresswell, 1996, p???]

It is the defining axiom of the system K (K is the weakest Normal system) [Hughes and Cresswell, 1996, p???]

It is part of all regular logic systems. [Chellas, 1980, p235]

Systems

T = K + T [Lp>p]

D = K + D [Lp>Mp]

B = K + T [Lp>p] + B [p>LMp]

S4 = K + T [Lp>p] + 4 [Lp > LLp]

S5 = K + T [Lp>p] + 5 [Mp>LMp]


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