Pledger's S3 extension 10r

[Pledger, 1972]


This system has 10 distinct proper affirmative modalities (plus the improper modality p) and is contained in S5 but not 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
MMp                          implied by Mp, MLMp, MMLp

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

LLMp  implied by LLp         it implies LMp
MMLp  it implies MMp         implied by MLp

LMLp  implied by Lp, LLp     it implies LMp, MLp
MLMp  it implies Mp, MMp     implied by MLp, LMp

[Pledger, 1972, p270-271]

Based on

The system 10r is: the system S3 plus any one of the following sets:

   {LLMLp => p, LMMp => Mp}
or {p => MMLMp,  Lp => MLLp}

[Pledger, 1972, p273]

Basis for

10ra = 10r + MMp

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