Pledger's S3 extension 18r

[Pledger, 1972]

Notes

This system has 18 distinct proper affirmative modalities, plus the improper modality p, and is contained in neither K2 nor S5. [Pledger, 1972, p270-271]

The distinct affirmative modalities of the system are:

p       implied by Lp            it implies Mp

Lp      implied by LLp           it implies p, LMLp
Mp      it implies MMp           implied by p, MLMp

LLp                              it implies Lp, LLMp, LMLLp
MMp                              implied by Mp, MMLp, MLMMp

LMp     implied by LMLp, LMLLMp  it implies LMMp, MLMp
MLp     it implies MLMp, MLMMLp  implied by LMLp, MLLp

LLMp    implied by LLp           it implies LMLLMp
MMLp    it implies MMp           implied by MLMMLp

LMLp    implied by Lp, LMLLp     it implies LMp, MLp, LMMLp
MLMp    it implies Mp, MLMMp     implied by LMp, MLp, MLLMp

LMMp    implied by LMp, LMMLp    it implies MLMMp
MLLp    it implies MLp, MLLMp    implied by LMLLp

LMLLp   implied by LLp           it implies LMLp, MLLp, LMLLMp
MLMMp   it implies MMp           implied by LMMp, MLMp, MLMMLp

LMMLp   implied by LMLp          it implies LMMp, MLMMLp
MLLMp   it implies MLMp          implied by MLLp, LMLLMp

LMLLMp  implied by LLMp, LMLLp   it implies LMp, MLLMp
MLMMLp  it implies MMLp, MLMMp   implied by MLp, LMMLp

[Pledger, 1972, p270-271]

Based on

The system 18r is: the system S3 plus any one of the following:

[Pledger, 1972, p275]

Basis for

18ra is 18r + MMp [Pledger, 1972, p279]

18rb is 18r + MLMMp [Pledger, 1972, p279]


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