# Pledger's S3 extension 14r

[Pledger, 1972]

## Notes

This system has 14 distinct proper affirmative modalities, (plus the improper modality p) and is contained in S5. but not in 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, MLLp
MMp                           implied by Mp, LMMp, MLMp, MMLp

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

LLMp   implied by LLp         it implies LMp, MLLMp
MMLp   it implies MMp         implied by MLp, LMMLp

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

LMMp   implied by LMp, LMMLp  it implies MMp
MLLp   it implies MLp, MLLMp  implied by LLp

LMMLp  implied by LMLp        it implies LMMp, MMLp
MLLMp  it implies MLMp        implied by LLMp, MLLp
```

[Pledger, 1972, p270-271]

## Based on

The system 14r is: the system S3 plus any one of the following:

• Necessity based
1. LMLLp => p
2. LMLLp => Lp
3. LMLLp => LLp
• Possibility based
1. p => MLMMp
2. Lp => MLMMp
3. LLp => MLMMp

(You can see the part duality plays here.) [Pledger, 1972, p275]

## Basis for

14rb = 14r + either of: