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Single Idea 13136

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

Full Idea

A 'prefix' is a finite sequence of positive integers. A 'prefixed formula' is an expression of the form σ X, where σ is a prefix and X is a formula. A prefix names a possible world, and σ.n names a world accessible from that one.

Gist of Idea

The prefix σ names a possible world, and σ.n names a world accessible from that one

Source

M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 2.2)

Book Ref

Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.48

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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]