[Hughes and Cresswell, 1996]
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]
The system S4M is S4 + the axiom MS [LMp>MLp] [Hughes and Cresswell, 1996, p131]
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
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This page was last modified on September 29th, 2005