# 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
- LMLLp => p
- LMLLp => Lp
- LMLLp => LLp

- Possibility based
- p => MLMMp
- Lp => MLMMp
- LLp => MLMMp

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

## Basis for

14rb = 14r + either of:

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© Copyright 2000, by John Halleck, All Rights Reserved.

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This page was last modified on November 21st, 2004