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Full Idea
System D is usually thought of as Deontic Logic, concerning obligations and permissions. □P → P is not valid in D, since just because an action is obligatory, it does not follow that it is performed.
Gist of Idea
□P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed
Source
M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.12.2 Ex)
Book Ref
Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.34
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] |