Pledger's S3 extension 8p

[Pledger, 1972]


This system has 8 distinct proper affirmative modalities (plus the improper modality p) and is in neither K2 nor S5 [Pledger, 1972, p270-271]

The distinct affirmative modalities of the syatem are:

p     implied by Lp       it implies Mp

Lp    implied by LLp      it implies p, LMp, MLp, LMMp
Mp    it implies MMp      implied by p, MLp, LMp, MLLp

LLp                       it implies Lp, LMp, MLLp
MMp                       implied by Mp, MLp, LMMp

LMp   implied by Lp, LLp  it implies Mp, LMMp
MLp   it implies Mp, MMp  implied by Lp, MLLp

LMMp  implied by Lp, LMp  it implies MMp
MLLp  it implies Mp, MLp  implied by LLp

[Pledger, 1972, p270-271]

Based on

The system 8p is: the system S3 plus one of the following sets:

{ LLMp => p, LMLp => p } or the dual
{ p => MMLp, P => MLMp }

[Pledger, 1972, p275]

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