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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