Sentence examples for a valid derivation from inspiring English sources
Then to check whether \(\mathcal{D}\) is a valid derivation, it suffices to check whether each of its \(n\) lines (where \(n \lt \lvert \mathcal{D}\rvert\) – the size of \(\mathcal{D}\) under a suitable binary encoding) is an axiom of \(\mathsf{ZFC}\) or follows from earlier lines by modus ponens or universal generalization.
In addition to being able to provide strictly valid derivations, the system is also able to produce derivations which are only likely valid, accompanied by an associated confidence.
Proofs nets, so defined, can then be show to be the graphs that correspond to valid derivations.
The latter derivation structure is J-valid as being composed of the J-valid derivation structure D′ and J-valid rules (∧ elimination and → elimination are J-valid, because sr and sr are in J ).
It thus follows that the following problem is in \ \textbf{NP}\): \(n\text\sc{PROVABILITY}_{\mathsf{T}}\ \) Given a formula \ \phi\) in the language of \(\mathsf{T}\) and a natural number \(n\), does there exist a valid \(\mathsf{T}\ -derivation \(\maT}\ -derivationength \(\mathcal{such that \(\mathcal{D}\) is a valid proff of \(\phi\)?
This derivation is J-valid, as it is the result of a composition of the J-valid derivations D1′ and D2.
As an alternative to CT scanning, laser Doppler flowmetry has recently been introduced as a valid method of determining bone vascularity and, as a derivation, bone quality [ 38].
"A valid point," Alec said.
