# Pledger's S3 extension 8p

[Pledger, 1972]

## Notes

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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