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Full Idea
For modal logic we add to the syntax of classical logic two new unary operators □ (necessarily) and ◊ (possibly).
Gist of Idea
Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic
Source
M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.3)
Book Ref
Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.5
9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |