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