# Pledger's S3 extension 10p

[Pledger, 1972]

## Notes

This system has 10 distinct proper affirmative modalities (plus the
improper modality p) and is contained in neither
S5 nor 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, LMp, MLLp, LMLp
MMp implied by Mp, MLp, LMMp, MLMp
LMp implied by LLp, LMLp it implies LMMp, MLMp
MLp it implies MMp, MLMp implied by MLLp, LMLp
LMLp implied by Lp, LLp it implies LMp, MLp, LMMp
MLMp it implies Mp, MMp implied by LMp, LMp, MLLp
LMMp implied by LMp, LMLp it implies MMp
MLLp it implies MLp, MLMp implied by LLp

[Pledger, 1972, p270-271]

## Based on

The system 10p is: the system S3 plus any
one of the following (Arranged as axiom, dual of axiom):

LMLLMp => p p => MLMMLp
LMLLMp => Lp Mp => MLMMLp
LMLLMp => LLp MMp => MLMMLp

[Pledger, 1972, p273]

## Basis fors

10pb = 10p + MMp

10pb = 10p + MLMMp

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This page was last modified on November 21st, 2004