# Pledger's S3 extension 10r

[Pledger, 1972]

## Notes

This system has 10 distinct proper affirmative modalities (plus the
improper modality p) and is contained in
S5 but not 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
MMp implied by Mp, MLMp, MMLp
LMp implied by LLMp, LMLp it implies MLMp
MLp it implies MLMp, MMLp implied by LMLp
LLMp implied by LLp it implies LMp
MMLp it implies MMp implied by MLp
LMLp implied by Lp, LLp it implies LMp, MLp
MLMp it implies Mp, MMp implied by MLp, LMp

[Pledger, 1972, p270-271]

## Based on

The system 10r is: the system S3 plus any
one of the following sets:

{LLMLp => p, LMMp => Mp}
or {p => MMLMp, Lp => MLLp}

[Pledger, 1972, p273]

## Basis for

10ra = 10r + MMp

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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