# Pledger's S3 extension 8q

[Pledger, 1972]

## Notes

This system has 8 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, LMp
Mp it implies MMp implied by p, MLp
LLp it implies Lp, LLMp
MMp implied by Mp, MMLp
LMp implied by Lp, LLMp it implies MLp
MLp it implies Mp, MMLp implied by LMp
LLMp implied by LLp it implies LMp
MMLp it implies MMp implied by MLp

[Pledger, 1972, p270-271]

## Based on

The system 8q is: the system S3 plus any
one of the following: (Arranged as axiom, dual of axiom)

LMp => LMLLp MLMMp => LMp
LMp => LMLp MLMp => LMp
LMp => MLLp LMMp => MLp
LMp => MLp self dual
LMM => LMLLp MLMMp => MLLp
LMM => LMLp MLMp => MLLp
LMM => MLLp LMMp => MLLp
LMM => MLp LMp => MLLp

[Pledger, 1972, p275]

## Basis for

8qa = 8q + MMp (Axiom S)

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This page was last modified on November 21st, 2004