What is accessibility relation?

Accessibility Relation

In modal logic, an accessibility relation is a binary relation, written as between possible worlds.

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Some articles on accessibility relation:

Modal Logic - Formalizations - Semantics
... consists of a non-empty set, G, whose members are generally called possible worlds, and a binary relation, R, that holds (or not) between the possible ... This binary relation is called the accessibility relation ... We do so by defining a relation ⊨ between possible worlds and propositional letters ...
Kripke Semantics - Model Constructions
... of Kripke frames and is a mapping such that f preserves the accessibility relation, i.e ... In general, a bisimulation between frames and is a relation B ⊆ W × W’, which satisfies the following “zig-zag” property if u B u’ and u R v, there exists v’ ∈ W’ such that v ... The definition of the accessibility relation R’ varies in the simplest case we put , but many applications need the reflexive and/or transitive closure of this relation ...
Accessibility Relation - Computer Science Applications
... Either choice defines a particular 'accessibility relation' giving rise to a particular modal logic suited specifically for theorems about the computation ...

Famous quotes containing the word relation:

    In relation to God, we are like a thief who has burgled the house of a kindly householder and been allowed to keep some of the gold. From the point of view of the lawful owner this gold is a gift; From the point of view of the burglar it is a theft. He must go and give it back. It is the same with our existence. We have stolen a little of God’s being to make it ours. God has made us a gift of it. But we have stolen it. We must return it.
    Simone Weil (1909–1943)