Full Idea
Modern modal logic takes into consideration the way the modal relates the possible worlds, called the 'accessibility' relation. .. We let R be the accessibility relation, and xRy reads as 'y is accessible from x.
Clarification
[R is usually printed in a script font]
Gist of Idea
Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x'
Source
M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 1.5)
Book Reference
Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.9
A Reaction
There are various types of accessibility, and these define the various modal logics.