# Pledger's S3 extension 18r

[Pledger, 1972]

## Notes

This system has 18 distinct proper affirmative modalities,
plus the improper modality p, and is contained in neither
K2 nor 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, LMLLp
MMp implied by Mp, MMLp, MLMMp
LMp implied by LMLp, LMLLMp it implies LMMp, MLMp
MLp it implies MLMp, MLMMLp implied by LMLp, MLLp
LLMp implied by LLp it implies LMLLMp
MMLp it implies MMp implied by MLMMLp
LMLp implied by Lp, LMLLp it implies LMp, MLp, LMMLp
MLMp it implies Mp, MLMMp implied by LMp, MLp, MLLMp
LMMp implied by LMp, LMMLp it implies MLMMp
MLLp it implies MLp, MLLMp implied by LMLLp
LMLLp implied by LLp it implies LMLp, MLLp, LMLLMp
MLMMp it implies MMp implied by LMMp, MLMp, MLMMLp
LMMLp implied by LMLp it implies LMMp, MLMMLp
MLLMp it implies MLMp implied by MLLp, LMLLMp
LMLLMp implied by LLMp, LMLLp it implies LMp, MLLMp
MLMMLp it implies MMLp, MLMMp implied by MLp, LMMLp

[Pledger, 1972, p270-271]

## Based on

The system 18r is: the system S3 plus any
one of the following:

- Necessity based:
- LLMLp => p
- LLMLp => Lp
- LLMLp => LLp

- Possibility based:
- p => MMLMp
- Mp => MMLMp
- MMp => MMLMp

[Pledger, 1972, p275]

## Basis for

18ra is 18r + MMp
[Pledger, 1972, p279]

18rb is 18r + MLMMp
[Pledger, 1972, p279]

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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