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Full Idea
In D we add to K a new axiom saying that 'what's necessary is possible' (□φ→◊φ), ..and it can then be proved that tautologies are possible and contradictions are not necessary.
Gist of Idea
In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary
Source
Theodore Sider (Logic for Philosophy [2010], 6.4.2)
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.166
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] |