Concept
Branching
A point at which an argument or a construction splits into cases that must all be handled. In a proof tree it is where a formula forces one of two things rather than both, and it is what makes the tree grow in width rather than in depth.
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The tree that closes
To prove a formula, assume it false and take it apart. Every branch ends in a contradiction, or one of them describes exactly how it could have been false — and either way the tree is the answer, drawn.
The assumption a proof pays back
A tableau assumes the opposite once and takes it apart. Natural deduction assumes things freely, uses them, and then withdraws them — and the withdrawal is what turns a derivation of a consequence into a proof of an implication.
Named alongside it
The objects these essays reach for when they reach for this one.
CompletenessProof systemSoundnessTableauDecision procedureDischargeImplicationLiteralNatural deductionRefutationSatisfiability