* Soundness: if the string is not in the language, no prover, however malicious, will be able to convince the verifier to accept the string with probability exceeding 1 / 3.

# Soundness: if the statement is false, no cheating prover can convince the honest verifier that it is true, except with some small probability.

Soundness is among the most fundamental properties of mathematical logic.

Soundness properties come in two main varieties: weak and strong soundness, of which the former is a restricted form of the latter.

Soundness of a deductive system is the property that any sentence that is provable in that deductive system is also true on all interpretations or structures of the semantic theory for the language upon which that theory is based.

* ( Soundness ) Every provable second-order sentence is universally valid, i. e., true in all domains under standard semantics.

* Soundness, a logical term meaning that an argument is valid and its premises are true

Soundness guarantees that all possible behaviours are preserved while completeness guarantees that no behaviour is added by the encoding.

* Soundness: If x ∉ L then for every π, V < sup > π </ sup >( x ) accepts with probability at most s ( n ).

Validity and Soundness in the Internet Encyclopedia of Philosophy.

In Quality of Management they scored second place, third in Long Term Investments, fourth in Financial Soundness, and ninth in Global Competitiveness.

It was established by the Federal Housing Enterprises Financial Safety and Soundness Act of 1992.

You must attach a statement to your return, if you take advantage of this automatic extension, showing that you were in Alaska or were outside the United States or Puerto Rico on April 15 or other due date.

Within certain wide limits anatomy dictates function and, if one is permitted to speculate, potential pathology should be included in this statement as well.

For instance, the following statement was rated low in compulsivity, `` She's naturally quite neat about things, but it doesn't bother her at all if her room gets messy.

And the more complex the morphophonemic system is in relation to the phonemic base, the less easily a phonemic system will be analysed without close attention to the morphophonemics -- at least, the less satisfying will a phonemic statement be if it cannot be related through morphophonemic rules to grammatically meaningful structures.

In many cases that statement -- `` We break even on our downtown operation and make money on our branches '' -- would be turned around if the cost analysis were recalculated on terms less prejudicial to the old store.

If he is not told which of four or five readings was meant for him, he can more readily assess each item in a larger frame: `` Does that statement really sound as if it were for me, significant in my particular life??

After reading his statement discharging the 23d ward case, Karns told Wexler that if the seven cases scheduled for trial also involved persons who had been subpenaed, he would dismiss them.

The statement explained that under the Georgia Constitution and state law, tax-exempt status is granted to educational institutions only if they are segregated.

Compare this statement of a nineteenth-century judge with how Congressman Martin, according to the Daily Labor Report of Sept. 19, 1961, defends the necessity of enacting anti-trust legislation in the field of labor `` if we wish to prevent monopolistic fixing of wages, production or prices and if we wish to preserve the freedom of the employer and his employees to contract on wages, hours and conditions of employment ''.

the startling statement in a respectable periodical that `` Catholics, if the present system is still in operation, will constitute almost one-third of the House of Lords in the next generation '' ; ;

B attempts to falsify A's conditional statement (" if Republican then against gun control ") by providing evidence he believes would contradict its implication.

However, the opposite can also be true-An opponent can turn a positive statement into a bad one, if the speaker uses ambiguity ( intentionally or not ).

Thus, intuitionists are ready to accept a statement of the form " P or Q " as true only if we can prove P or if we can prove Q:

In the statement < code >< u > if </ u > token = if < u > then </ u > < u > result </ u >

Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S < sup > n </ sup > → ℝ < sup > n </ sup > that does not equalize on any antipodes then we can construct a map g: S < sup > n </ sup > → S < sup > n-1 </ sup > by the formula

In this case, if a proof uses this statement, researchers will often look for a new proof that doesn't require the hypothesis ( in the same way that it is desirable that statements in Euclidean geometry be proved using only the axioms of neutral geometry, i. e. no parallel postulate.

If the ideals A and B of R are coprime, then AB = A ∩ B ; furthermore, if C is a third ideal such that A contains BC, then A contains C. The Chinese remainder theorem is an important statement about coprime ideals.

Ike's sense of responsibility was underscored by his draft of a statement to be issued if the invasion failed ; it has been called one of the great speeches of history:

It is the inference that if a statement implies a statement and a statement also implies, then if either or is true, then has to be true.

`` That is, if we can be sure this is Colcord's money '' --

Let me pass over the trip to Sante Fe with something of the same speed which made Mrs. Roebuck `` wonduh if the wahtahm speed limit '' ( 35 m.p.h. ) `` is still in ee-faket ''.

It is the last of the three tests of manhood which the women impose, to discover if a male is worthy of survival there.

There was a measure of protection in its concrete walls and ceiling, but the engineers who hastily installed it were well aware that concrete is not much better than prayer, if as efficacious, when a direct hit comes along.

`` And if the dive goes OK he has the exclusive import rights to your line for this country, is that right ''??

`` All right, if you can't do your arithmetic during school hours you can do it after school is out '', Miss Langford said firmly, not smiling.

Why, in the first place, call himself a liberal if he is against laissez-faire and favors an authoritarian central government with womb-to-tomb controls over everybody??

And if he is so scornful of the rights of states, why not advocate a different sort of constitution that he could more sincerely support??

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

I think it is essential, however, to pinpoint here the difference between the two concepts of sovereignty that went to war in 1861 -- if only to see better how imperative is our need today to clarify completely our far worse confusion on this subject.

Unruly hair goes straight up from his forehead, standing so high that the top falls gently over, as if to show that it really is hair and not bristle.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

He will not curb his instinctual desires but release the energy within him that makes him feel truly and fully alive, even if it is only for this brief moment before the apocalypse of annihilation explodes on earth.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

And if I have gone into so much detail about so small a work, that is because it is also so typical a work, representing the germinal form of a conflict which remains essential in Mann's writing: the crude sketch of Piepsam contains, in its critical, destructive and self-destructive tendencies, much that is enlarged and illuminated in the figures of, for instance, Naphta and Leverkuhn.

All such imitations of negative quality have given rise to a compensatory response in the form of a heroic and highly individualistic humanism: if man can neither know nor love reality as it is, he can at least invent an artistic `` reality '' which is its own world and which can speak to man of purely personal and subjective qualities capable of being known and worthy of being loved.

But Aristotle kept the principle of levels and even augmented it by describing in the Poetics what kinds of character and action must be imitated if the play is to be a vehicle of serious and important human truths.

Operating as a one man police force in fact if not in name, he is at once more independent and more dedicated than the police themselves.