more from M Fitting/R Mendelsohn

Single Idea 13142

[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 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,