Pledger's S3 extension 12q

[Pledger, 1972]

Notes

This system has 12 distinct proper affirmative modalities (plus the improper modality p) and is contained in K2 but not in 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, LMLp
Mp    it implies MMp         implied by p, MLMp

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

LMp   implied by LLMp, LMLp  it implies LMMp, MLMp
MLp   it implies MLMp, MMLp  implied by MLLp, LMLp

LLMp  implied by LLp         it implies LMp, LMLp, MLLp
MMLp  it implies MMp         implied by MLp, LMMp, LMMp

LMLp  implied by Lp, LLMp    it implies LMp, MLp, LMMp
MLMp  it implies Mp, MMLp    implied by MLp, LMp, MLLp

LMMp  implied by LMp, LMLp   it implies MMLp
MLLp  it implies MLp, MLMp   implied by LLMp

[Pledger, 1972, p270-271]

Based on

The system 12q is: the system S3 plus any one of the following: (Arranged as axiom, dual of axiom)

LMLLMp => LLMLp, MMLMp => MLMMLp

[Pledger, 1972, p275]

Basis for

12qb = 12q +


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