He first noted the relationship between conditions on accessibility relations and Lewis-style axioms for modal logic.

For example, and refer to an accessibility relation and and to in the model.

For each modal operator, one needs to transition from a world in the model to a world that is accessible through the accessibility relation.

The different systems of modal logic are distinguished by the properties of their corresponding accessibility relations.

Axiom T expresses reflexivity of the accessibility relation: every world is accessible from itself.

The 'accessibility relation' is a relationship between two 'possible worlds.'

These axioms describing the relationship between 'possible worlds' is the 'accessibility relation' in detail.

One of the applications of 'possible worlds' semantics and the 'accessibility relation' is to physics.

There are other applications of the 'accessibility relation' in philosophy.

Yet another example of the use of the 'accessibility relation' is in deontic logic.