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### Single Idea 14973

#### [catalogued under 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5]

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 Reference

'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.141