Accessibility relation

In modal logic, an accessibility relation R {displaystyle R} is a binary relation such that R ⊆ W × W {displaystyle Rsubseteq W imes W} where W {displaystyle W} is a set of possible worlds. The accessibility relation determines for each world w ∈ W {displaystyle win W} which worlds w ′ {displaystyle w'} are accessible from w {displaystyle w} . If a possible world w ′ {displaystyle w'} is accessible from w {displaystyle w} we usually write w R w ′ {displaystyle wRw'} (or sometimes R w w ′ {displaystyle Rww'} ). In modal logic, an accessibility relation R {displaystyle R} is a binary relation such that R ⊆ W × W {displaystyle Rsubseteq W imes W} where W {displaystyle W} is a set of possible worlds. The accessibility relation determines for each world w ∈ W {displaystyle win W} which worlds w ′ {displaystyle w'} are accessible from w {displaystyle w} . If a possible world w ′ {displaystyle w'} is accessible from w {displaystyle w} we usually write w R w ′ {displaystyle wRw'} (or sometimes R w w ′ {displaystyle Rww'} ). A statement in logic refers to a sentence (with a subject, predicate, and verb) that can be true or false. So, 'The room is cold' is a statement because it contains a subject, predicate and verb, and it can be true that 'the room is cold' or false that 'the room is cold.'