more from M Fitting/R Mendelsohn

### Single Idea 13143

#### [catalogued under 4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / c. Derivation rules of ML]

Full Idea

General tableau rules for universal modality: a) if σ ¬◊ X then σ.m ¬X b) if σ □ X then σ.m X , where m refers to a world that can be seen (rather than introducing a new world).

Gist of Idea

Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists]

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 universal rule of □, usually read as 'necessary', only refers to worlds which can already be seen, whereas possibility (◊) asserts some thing about a new as yet unseen world.