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
The system 18r is: the system S3 plus any one of the following:
18ra is 18r + MMp [Pledger, 1972, p279]
18rb is 18r + MLMMp [Pledger, 1972, p279]
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