System S4.4 (Sobociński)

[Zeman, 1973]

Notes

Based on

System S4.4 is system S4 Plus the axiom M16 [p=>(MLp>Lp)] [Zeman, 1973, p249]

System S4.4 is system S4 Plus the axiom HCR1 [MLp>(p>Lp)] [Hughes and Cresswell, 1996, p362]

Basis for

Sobociński's K4 is the system S4.4 plus the axiom MS [LMp=>MLp] [Zeman, 1973, p249]

If a formula is a theorem of S5, but not of S4.4, and has only one variable, its addition to S4.4 gives S5. [Zeman, 1973, p266]

System S4.9 is S4.4 + M18 [ MLp>p+(LMq>MLq) ] [Zeman, 1973, p266] [Hughes and Cresswell, 1996, p362]


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