Definition
Branching time is a model in which time is not a single line but a tree. The past is a settled trunk — one fixed sequence of moments leading to now — but the future fans out into many branches, each a different way things could go from here.
The model captures a strong intuition: the past is closed, the future is open. Whatever happened, happened; but what will happen is, in some genuine sense, not yet decided. Branching time gives that intuition a precise structure within tense logic.
Why it matters
How it works
On a branching model, each moment has a unique chain of predecessors but possibly many successors. A statement about the future is then ambiguous: 'there will be a sea battle tomorrow' might mean it happens on every branch, on some branch, or on the branch actually realised.
This resolves an old puzzle stretching back to Aristotle. If 'there will be a sea battle tomorrow' is already determinately true today, the future seems fixed and choice an illusion. Branching time lets such a future-contingent statement be neither determinately true nor determinately false now — it becomes settled only once a branch is taken. The model thereby weaves together tense logic and the logic of possibility: a future branch is exactly a way the world could still go.