Pledger's S3 extension 10p

[Pledger, 1972]


This system has 10 distinct proper affirmative modalities (plus the improper modality p) and is contained in neither S5 nor 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, LMp, MLLp, LMLp
MMp                         implied by Mp, MLp, LMMp, MLMp

LMp   implied by LLp, LMLp  it implies LMMp, MLMp
MLp   it implies MMp, MLMp  implied by MLLp, LMLp

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

LMMp  implied by LMp, LMLp  it implies MMp
MLLp  it implies MLp, MLMp  implied by LLp

[Pledger, 1972, p270-271]

Based on

The system 10p is: the system S3 plus any one of the following (Arranged as axiom, dual of axiom):

LMLLMp => p      p => MLMMLp
LMLLMp => Lp    Mp => MLMMLp
LMLLMp => LLp  MMp => MLMMLp

[Pledger, 1972, p273]

Basis fors

10pb = 10p + MMp

10pb = 10p + MLMMp

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