System S3.5 (Åqvist)

Notes

[Hughes and Cresswell, 1996] mention a system S3.3 (originally investigated by Feys, which was later shown to be system S3.5 itself. [Pledger 1972, sec 6, p276] [Pledger 2001]

This system has also been called S3(S) [Pledger 2000]

This system is system 12r (Pledger) enumeration of systems containing S3 [Pledger, 1972]

This system has 12 distinct proper postive modalities (and the improper modality p). They are:

p implied by Lp it implies Mp Lp implied by LLp it implies p, LMp, MLp, LMMLp Mp it implies MMp implied by p, LMp, MLp, MLLMp LLp it implies Lp, LLMp, MLLp MMp implied by Mp, LMMp, MMLp LMp implied by Lp, LLMp it implies Mp, LMMp MLp it implies Mp, MMLp implied by Lp, MLLp LLMp implied by LLp it implies LMp, MLLMp MMLp it implies MMp implied by MLp, LMMLp LMMp implied by LMp, LMMLp it implies MMp MLLp it implies MLp, MLLMp implied by LLp LMMLp implied by Lp it implies LMMp, MMLp MLLMp it implies Mp implied by LLMp, MLLp