Ideas from 'works' by C.I. Lewis [1935], by Theme Structure

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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
The simplest of the logics based on possible worlds is Lewis's S5 [Girle]
10. Modality / A. Necessity / 2. Nature of Necessity
Equating necessity with informal provability is the S4 conception of necessity [Read]