Full Idea
System D serial rules (also for T, B, S4, S5): a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X
Gist of Idea
D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X
Source
M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.3)
Book Reference
Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.52