This system has 14 distinct proper affirmative modalities, (plus the improper modality p) and is contained in S5. but not in K2. [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, LMLp, MLLp MMp implied by Mp, LMMp, MLMp, MMLp LMp implied by LLMp, LMLp it implies LMMp, MLMp MLp it implies MLMp, MMLp implied by LMLp, MLLp LLMp implied by LLp it implies LMp, MLLMp MMLp it implies MMp implied by MLp, LMMLp LMLp implied by Lp, LLp it implies LMp, MLp, LMMLp MLMp it implies Mp, MMp implied by LMp, MLp, MLLMp LMMp implied by LMp, LMMLp it implies MMp MLLp it implies MLp, MLLMp implied by LLp LMMLp implied by LMLp it implies LMMp, MMLp MLLMp it implies MLMp implied by LLMp, MLLp
The system 14r is: the system S3 plus any one of the following:
(You can see the part duality plays here.) [Pledger, 1972, p275]
14rb = 14r + either of:
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