Pledger's S3 extension 16s

[Pledger, 1972]

Pledger's 16s is Sobociński's 3.01 [Sobociński, 1976a]


This system has 16 distinct proper affirmative modalities, (Plus the improper modality p) and is contained in both S5 amd K2. [Pledger, 1972, p270-271]

The distinct affirmative modalities of the system 16s 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, LLMLp/LMLLp
MMp                                      implied by Mp, MLMMp/MMLMp

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

LLMp         implied by LLMLp/LMLLp      it implies LMp, MLLMp
MMLp         it implies MLMMp/MMLMp      implied by MLp, LMMLp

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

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

LLMLp/LMLLp  implied by LLp              it implies LLMp, LMLp, MLLp
MLMMp/MMLMp  it implies MMp              implied by LMMp, MLMp, MMLp

LMMLp        implied by LMLp             it implies LMMp, MMLp
MLLMp        it implies MLMp             implied by LLMp, MLLp

[Pledger, 1972, p270-271]

Based on

The system 16s is: the system S3 plus any one of the following:

[Pledger, 1972, p275]

Basis for

16sb = 16s plus either of

[Pledger, 1972, p279]

Based on

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