# System S4M

[Hughes and Cresswell, 1996]

## Notes

This system is called K1 by Sobociński, and is the basis for most
of his K systems.
[Hughes and Cresswell, 1996, p364]

This system was called M by Scott and Lemon. It was called S4.1 by
McKinsey, but is not contained within
S4.2. and so isn't deserving of the name.
[Hughes and Cresswell, 1996, p143 (ch7, fn7)]

This system is Ken Pledger's system 4q.
[Pledger, 1972, p270]
It has 4 distinct proper affirmative modalities, and the improper modality
p. They are related as follows

p implied by Lp it implies Mp
Lp it implies p, LMp
Mp implied by p, MLp
LMp implied by Lp it implies MLp
MLp it implies Mp implied by LMp

[Pledger, 1972, p270]

This is often a temporal system, with La meaning
"'a' is and always will be".

Characterized by final reflexive frames.
[Hughes and Cresswell, 1996, p362]

## Based on

The system S4M is S4 + the axiom
MS [LMp>MLp]
[Hughes and Cresswell, 1996, p131]

## Or

The system S4m == K1 is the system S3 plus any of
the following (Arranged as axiom, dual of axiom):

LMp => LLMLp, MMLMp => MLp
LMMp => LLMLp, MMLMp => MLLp

## Basis for

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This page was last modified on September 29th, 2005