Pledger's S3 extension 14q

[Pledger, 1972]

Notes

This system has 14 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 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
MMp                            implied by Mp, MMLp

LMp    implied by LMLp, LMLLp  it implies LMMp, MLMp
MLp    it implies MLMp, MLMMp  implied by LMLp, MLLp

LLMp   implied by LLp          it implies LMLLp
MMLp   it implies MMp          implied by MLMMp

LMLp   implied by Lp, LMLLp    it implies LMp, MLp, LMMp
MLMp   it implies Mp, MLMMp    implied by LMp, MLp, MLLp

LMMp   implied by LMp, LMLp    it implies MLMMp
MLLp   it implies MLp, MLMp    implied by LMLLp

LMLLp  implied by LLMp         it implies LMp, LMLp, MLLp
MLMMp  it implies MMLp         implied by MLp, LMMp, MLMp

[Pledger, 1972, p270-271]

Based on

The system 14q is: the system S3 plus any one of the following: (Arranged as axiom, dual of axiom)

LMp => LMMLp, MLLMp => MLp
LMp => MLMMLp, LMLLMp => MLp
LMp => MMLp, LLMp => MLp
LLMp => LLMLp, MMLMp => MMLp
LLMp => LMLLp, MLLMp => MMLp
LLMp => LMLp, MLMp => MMLp
LLMp => LMMLp, MLMMp => MMLp
LLMp => MLLp, LMMp => MMLp
LLMp => MLMMLp, LMLLMp => MMLp
LMMp => LMMLp, LLMp => MLLp
LMMp => MLMMLp, LMLLMp => MLLp
MLMp => MLMMLp, LMLLMp => LMLp
MLLMp => MLMMLp, LMLLMp => LMMLp
MLMMp => MLMMLp, LMLLMp => LMLLp
LMLLMp => MLMMLp, self dual

[Pledger, 1972, p275]

Basis for

14qa is 14q + MMp

14qb is 14q + MLMMp

Pledger's S3 extension 14q

Notes

Based on

Basis for

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