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Full Idea
S5 contains the four main reduction laws, so the first of any pair of operators may be deleted. Hence all but the last modal operator may be deleted. This leaves six modalities: p, ◊p, □p, and their negations.
Gist of Idea
In S5 all the long complex modalities reduce to just three, and their negations
Source
Max J. Cresswell (Modal Logic [2001], 7.1.2)
Book Ref
'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.141
| 14970 | Normal system K has five axioms and rules [Cresswell] |
| 14971 | D is valid on every serial frame, but not where there are dead ends [Cresswell] |
| 14972 | S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell] |
| 14973 | In S5 all the long complex modalities reduce to just three, and their negations [Cresswell] |
| 14974 | A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell] |
| 14975 | A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world [Cresswell] |
| 14976 | Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds [Cresswell] |