An accessibility relation is a relation which plays a key role in assigning truth values to sentences in the relational semantics for modal logic. In relational semantics, a modal formula's truth value at a possible world.

Accessibility relations are motivated conceptually by the fact that natural language modal statements.

This idea can be extended to various applications of modal logic. In epistemic logic. In deontic logic. In the application of modal logic to computer science, possible worlds can be understood as representing possible states of a system and the accessibility relation can be understood as representing state transitions (see Kripke structure (model checking).

Different applications of modal logic can suggest different restrictions on admissible accessibility relations, which can in turn lead to different validities. The mathematical study of how validities are tied to conditions on accessibility relations is known as modal correspondence theory.

See also

• Propositional attitude

• Modal depth

References

• Gerla, G.; Transformational semantics for first order logic, Logique et Analyse, No. 117–118, pp.69–79, 1987.

• Fitelson, Brandon; Notes on "Accessibility" and Modality, 2003.

• Brown, Curtis; Propositional Modal Logic: A Few First Steps, 2002.

• Kripke, Saul; Naming and Necessity, Oxford, 1980.

• List of Logic Systems List of most of the more popular modal logics.