Sentence examples for formulas such that from inspiring English sources

As was proved by Kurt Gödel, a 20th-century Moravian-born American mathematical logician, these calculi, if consistent, always contain well-formed formulas such that neither they nor their negations can be derived (shown tautologous) by the rules of the calculus.

A skeptical solution for ⟨ O, C ¯, ψ ⟩, is a sequence of formulas such that φ1,…, φ n such that: 1. φ i ∈C i, for i≤n   2.

A credulous solution for ⟨ O, C ¯, ψ ⟩, is a sequence of formulas such that φ1,…, φ n such that: 1. φ i ∈C i, for i≤n   2.

A proof structure is a set of links over a finite set of formulas such that every formula is at most once the premise of a link and at most once the conclusion.

It can be proved by induction on the structure of (psi ) that (pi _{2,l}(psi )) and (pi _2 psi )) are sets of formulas such that, for any interpretation (mathcal {I}), (mathcal {I}models bigvee pi _{2,l}(psi )) iff (mathcal {I}models psi ), (mathcal {I}models bigwedge pi _2 psi )) iff (mathcal {I}models psi ).

To prove that, we depart from formulas (phi in mathcal {L}_{N}) without nesting, as it can be eliminated with a slight modification of Lemma 6: For every (phi in mathcal {L}_{N}), for a fixed (Nin mathbb {N}), there exists a θ∈L N in which all probabilistic formulas are not subformulas of another probabilistic formulas, such that ϕ is satisfiable if, and only if, θ is.

The equilibrium conductance G is obtained from the Landauer formula such that G = G 0 T (E), where G 0 is the quantum conductance with relationship.

And the application designer could choose their own weight vector to customise the formula such that it is suitable for the nature of their application.

This distance reflects the minimal change in the formula such that it holds for all perturbations.

The former consists of a minimal subset of the clauses of an unsatisfiable formula, such that if we remove these clauses the resulting formula becomes satisfiable.

For instance, with the MDRD formula, 12.1% of patients would be classified as having CKD stage 3 on their first and second tests but 2.2% would be reclassified as CKD stage 2 on retesting and 0.22% as CKD stage 4. Overall, there is more consistency with the CKD-EPI formula such that the classification would be unchanged for about 82% of patients using MDRD and about 85% of patients using CKD-EPI.