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redundant proof : ウィキペディア英語版
redundant proof

In mathematical logic, a redundant proof is a proof that has a subset that is a shorter proof of the same result. That is, a proof \psi of \kappa is considered redundant if there exists another proof \psi^ of \kappa^ such that \kappa^\subseteq\kappa (i.e. \kappa^ \;\text\; \kappa) and |\psi^|<|\psi| where |\varphi| is the number of nodes in \varphi.〔Fontaine, Pascal; Merz, Stephan; Woltzenlogel Paleo, Bruno. ''Compression of Propositional Resolution Proofs via Partial Regularization''. 23rd International Conference on Automated Deduction, 2011.〕
== Local redundancy ==

A proof containing a subproof of the shapes (here omitted pivots indicate that the resolvents must be uniquely defined)
: (\eta\odot\eta_1) \odot (\eta\odot\eta_2)\text \eta \odot (\eta_1 \odot (\eta\odot\eta_2))
is locally redundant.
Indeed, both of these subproofs can be equivalently replaced by the shorter subproof \eta \odot (\eta_1 \odot \eta_2 ). In the case of local redundancy, the pairs of redundant inferences having the same pivot occur close to each other in the proof. However, redundant inferences can also occur far apart in the proof.
The following definition generalizes local redundancy by considering inferences with the same pivot that occur within different contexts. We write \psi\left() to denote a proof-context \psi\left() with a single placeholder replaced by the subproof \eta.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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