Crossword clues for soundness
The Collaborative International Dictionary
Soundness \Sound"ness\, n. The quality or state of being sound; as, the soundness of timber, of fruit, of the teeth, etc.; the soundness of reasoning or argument; soundness of faith.
Syn: Firmness; strength; solidity; healthiness; truth; rectitude.
Douglas Harper's Etymology Dictionary
late 14c., from sound (adj.) + -ness.
Wiktionary
n. 1 (context uncountable English) The state or quality of being sound. 2 (context countable English) The result or product of being sound. 3 (context logic English) The property (of an argument) of not only being valid, but also of having true premises. 4 (context logic English) The property of a logical theory that whenever a wff is a theorem then it must also be valid. Symbolically, letting ''T'' represent a theory within logic ''L'', this can be represented as the property that whenever is true, then must also be true, for any wff ''φ'' of logic ''L''.
WordNet
n. a state or condition free from damage or decay [ant: unsoundness]
the quality of being prudent and sensible [syn: wisdom, wiseness]
the firmness and tone of healthy tissue; "his muscle firmness" [syn: firmness]
Wikipedia
In mathematical logic, a logical system has the soundness property if and only if its inference rules prove only formulas that are valid with respect to its semantics. In most cases, this comes down to its rules having the property of preserving truth, but this is not the case in general.
Soundness is a property of interactive proof systems that requires that no prover can make the verifier accept for a wrong statement y ∉ L except with some small probability. The upper bound of this probability is referred to as the soundness error of a proof system.
More formally, for every prover $(\tilde{\mathcal{P}})$, and every y ∉ L:
$\Pr[(\perp,(\text{accept}))\gets (\tilde{\mathcal{P}})(y) \leftrightarrow (\mathcal{V})(y)] < 2^{-80}.$The above definition uses the somewhat arbitrary soundness error 2. As long as the soundness error is bounded by a polynomial fraction of the potential running time of the verifier (i.e. ≤ 1/poly(∣y∣)), it is always possible to amplify soundness until the soundness error becomes negligible relative to the running time of the verifier. This is achieved by repeating the proof and accepting only if all proofs verify. After ℓ repetitions, a soundness error ε will be reduced to ε.
Usage examples of "soundness".
After more than a century of constant disintegration, division, and disunification, of a constant crisis arising from the autopathic Culture-disease of rationalist-materialism, the Culture came back once more to health and soundness, to Authority and Faith.
It is a work instinct with musicianly feeling, and its strength is borne out by the soundness and skill displayed in its construction.
Llangarlians had replaced those strange, forgotten people who had built the Stone Dances, this union had been one of great soundness.
After more than a century of constant disintegration, division, and disunification, of a constant crisis arising from the autopathic Culture-disease of rationalist-materialism, the Culture came back once more to health and soundness, to Authority and Faith.
There was no question, therefore, of soundness of limb, and when he underwent the form of examination no spot nor blemish was found on him.
I not believe a most learned mathematician, whose very style attests the soundness of his judgment?
All modern-day sorcerers have to struggle fiercely to gain soundness of mind.
He had some trouble at first with the inspectors over those four projecting rooms but by using strong girders and folding money he had been able to convince them of the soundness of his engineering.
He was in the pink of condition for his age, and even the texture of his long frock coat had a character of elastic soundness, as if it were a living tissue.
It should be moved to a museum as an example of the soundness of Starfleet structural engineering practices of the twenty-second and twenty-third centuries.
Saw it all, as if it were the engine of a truck he were taking apart behind the Superette, removing one part after another in his slow way, running a careful thumb over each to feel its essential soundness under the necessary grease.