Ideas from 'Modal Logic' by Max J. Cresswell [2001], by Theme Structure
[found in 'Blackwell Guide to Philosophical Logic' (ed/tr Goble,Lou) [Blackwell 2001,0631206930]].
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / b. System K
14970

Normal system K has five axioms and rules

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
14971

D is valid on every serial frame, but not where there are dead ends

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
14972

S4 has 14 modalities, and always reduces to a maximum of three modal operators

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
14973

In S5 all the long complex modalities reduce to just three, and their negations

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
14976

Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds

8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
14974

A relation is 'Euclidean' if aRb and aRc imply bRc

10. Modality / A. Necessity / 4. De re / De dicto modality
14975

A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world
