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Single Idea 14971

[filed under theme 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D ]

Full Idea

If a frame contains any dead end or blind world, then D is not valid on that frame, ...but D is valid on every serial frame.

Gist of Idea

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

Source

Max J. Cresswell (Modal Logic [2001], 7.1.1)

Book Ref

'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.140

The 7 ideas from 'Modal Logic'

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]