more from this thinker     |     more from this text

Single Idea 9735

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

Full Idea

A 'frame' consists of a non-empty set G, whose members are generally called possible worlds, and a binary relation R, on G, generally called the accessibility relation. We say the frame is the pair so that a single object can be talked about.

Clarification

[the G and R are usually printed in a script font]

Gist of Idea

A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R >

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 6 ideas with the same theme [definitions of the main concepts used in modal logic]:

14684 A world is 'accessible' to another iff the first is possible according to the second [Salmon,N]
9734 Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn]
9736 A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn]
9735 A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn]
9741 Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn]
13727 A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn]