Full Idea
General tableau rules for existential modality: a) if σ ◊ X then σ.n X b) if σ ¬□ X then σ.n ¬X , where n introduces some new world (rather than referring to a world that can be seen).
Gist of Idea
Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new]
Source
M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2)
Book Reference
Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.49
A Reaction
Note that the existential rule of ◊, usually read as 'possibly', asserts something about a new as yet unseen world, whereas □ only refers to worlds which can already be seen,