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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
14971 | D is valid on every serial frame, but not where there are dead ends [Cresswell] |
13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
13706 | Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider] |
13710 | In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider] |
19033 | Deontic modalities are 'ought-to-be', for sentences, and 'ought-to-do' for predicates [Vetter] |