This system has 8 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, LMp Mp it implies MMp implied by p, MLp LLp it implies Lp, LLMp MMp implied by Mp, MMLp LMp implied by Lp, LLMp it implies MLp MLp it implies Mp, MMLp implied by LMp LLMp implied by LLp it implies LMp MMLp it implies MMp implied by MLp
The system 8q is: the system S3 plus any one of the following: (Arranged as axiom, dual of axiom)
LMp => LMLLp MLMMp => LMp LMp => LMLp MLMp => LMp LMp => MLLp LMMp => MLp LMp => MLp self dual LMM => LMLLp MLMMp => MLLp LMM => LMLp MLMp => MLLp LMM => MLLp LMMp => MLLp LMM => MLp LMp => MLLp
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This page was last modified on November 21st, 2004