# Pledger's S3 extension 12q

[Pledger, 1972]

## Notes

This system has 12 distinct proper affirmative modalities (plus the
improper modality p) and is
contained in K2 but not in
S5
[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
MMp implied by Mp, MMLp
LMp implied by LLMp, LMLp it implies LMMp, MLMp
MLp it implies MLMp, MMLp implied by MLLp, LMLp
LLMp implied by LLp it implies LMp, LMLp, MLLp
MMLp it implies MMp implied by MLp, LMMp, LMMp
LMLp implied by Lp, LLMp it implies LMp, MLp, LMMp
MLMp it implies Mp, MMLp implied by MLp, LMp, MLLp
LMMp implied by LMp, LMLp it implies MMLp
MLLp it implies MLp, MLMp implied by LLMp

[Pledger, 1972, p270-271]

## Based on

The system 12q is: the system S3 plus any
one of the following: (Arranged as axiom, dual of axiom)

LMLLMp => LLMLp, MMLMp => MLMMLp

[Pledger, 1972, p275]

## Basis for

12qb = 12q +

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This page was last modified on November 21st, 2004