System S4.2

Notes

Characterized by convergent S4 frames. [Hughes and Cresswell, 1996, p134]

Has ten non-equivalent modalities, p, Lp, MLp, LMp, Mp, and their negations [four proper affirmative modalities.] They are related as follows:

p    implied by Lp   it implies Mp

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

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

[Pledger, 1972, p270] [Hughes and Cresswell, 1968, p261]

Based on

The system S4.2 is the result of S4 + G1 [MLp>LMp] [Hughes and Cresswell, 1996,p134]

The system S4.2 is the result of S3 and any of the following sets of axioms:

{ MLLp, MLp, MLMMLp, MMLp } => {LMLLp, LMLLp, LMLp, LMMLp }
{ MLMMp, MLMMp, MLMp, MLLMp } => {LMMp, LMp, LMLLMp, LLMp }

{MLLp, MLp, MLMMLp, MMLp} => { LMMp, LMp, LMLLMp, LLMp }
  (this set contains all of it's duals.}

[Pledger, 1972, p275]

Basis for

The system K2 is the result of system S4.2 + MS [LMp=>MLp] [Zeman, 1973, p277] [Hughes and Cresswell, 1996, p362]


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