more from Rod Girle

### Single Idea 7788

#### [catalogued under 4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic]

Full Idea

The four important logical equivalences in modal logic (the Modal Negation equivalences) are: ¬◊p↔□¬p, ◊¬p↔¬□p, □p↔¬◊¬p, and ◊p↔¬□¬p.

Gist of Idea

Modal logic has four basic modal negation equivalences

Source

Rod Girle (Modal Logics and Philosophy [2000], 1.2)

Book Reference

Girle,Rod: 'Modal Logics and Philosophy' [Acumen 2000], p.3

A Reaction

[Possibly is written as a diamond, necessarily a square] These are parallel to a set of equivalences between quantifiers in predicate logic. They are called the four 'modal negation (MN) equivalences'.