more from M Fitting/R Mendelsohn

### Single Idea 9741

#### [catalogued under 4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / b. Terminology of ML]

Full Idea

A relation R is 'reflexive' if every world is accessible from itself; 'transitive' if the first world is related to the third world (ΓRΔ and ΔRΩ → ΓRΩ); and 'symmetric' if the accessibility relation is mutual.

Gist of Idea

Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual)

Source

M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.7)

Book Reference

Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.17

A Reaction

The different systems of modal logic largely depend on how these accessibility relations are specified. There is also the 'serial' relation, which just says that any world has another world accessible to it.