more from this thinker     |     more from this text

Single Idea 9737

[filed under theme 4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / a. Symbols of ML ]

Full Idea

The symbol ||- is used for the 'forcing' relation, as in 'Γ ||- P', which means that P is true in world Γ.

Clarification

[There is actually no space between the second vertical line and the horizontal line]

Gist of Idea

The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ

Source

M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.6)

Book Ref

Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.12

The 4 ideas with the same theme [symbols which are distinctive of modal logic]:

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]