Soundness is among the most fundamental properties of mathematical logic.

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: if the statement is false, no prover, even if it doesn't follow the protocol, can convince the honest verifier that it is true, except with some small probability.

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

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

* 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.

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.

Its properties come solely from the power of unlimited recursion.

Although formal certification of his freedom from Burghley's control was deferred until May 1572, Oxford was finally granted the income of £ 666 which his father had intended him to have earlier, but properties set aside to pay his father's debts would not come his way for another decade.

Their trade was to come to an end with the period following the Napoleonic Wars, for the town became one of the most fashionable resorts in Britain, brought about by the so-called properties of seawater.

Employing the distinction, Henry gave up his right to invest his bishops and abbots, but reserved the custom of requiring them to come and do homage for the " temporalities " ( the landed properties tied to the episcopate ), directly from his hand, after the prelate had sworn homage and feudal vassalage in the ceremony called commendatio, the commendation ceremony, like any secular vassal.

Universal properties come in two types: initial properties and terminal properties.

Gouache paints come in many colors and are usually mixed with water to achieve the desired working properties and to control the opacity when dry.

He eventually returns to Amber, which is in mourning: the news has just come that Caine has been murdered, and Bleys injured, by a mystery assassin with a rifle-an assassin who demonstrates ( with a thrown bomb at Caine's funeral, which misses any other family members ) that he has access to something with explosive properties in Amber.

The name Muswell is believed to come from a natural spring or well ( the " Mossy Well "), said to have miraculous properties.

( Terrytoons and its properties were acquired by CBS in the 1950s, later spun off as part of Viacom, but have again come under CBS ownership as part of a series of corporate mergers and acquisitions.

From then on Reines dedicated the major part of his career to the study of the neutrino ’ s properties and interactions, which work would influence study of the neutrino for future researchers to come, including the discovery of neutrinos emitted from Supernova SN1987A by the Irvine-Michigan-Brookhaven Collaboration.

Cone snail venom, in more recent years, has come to interest biotechnologists and pharmacists because of its potential medicinal properties.

Other theoretical work contends that, " A sharp interface between quark matter and the vacuum would have very different properties from the surface of a neutron star "; and, addressing key parameters like surface tension and electrical forces that were neglected in the original study, the results show that as long as the surface tension is below a low critical value, the large strangelets are indeed unstable to fragmentation and strange stars naturally come with complex strangelet crusts, analogous to those of neutron stars.

The nature of the universe is air, limitless and eternal, from which, as it condenses and rarefies and changes its properties, the other forms come into being.

Employing the distinction, Henry gave up his right to invest his bishops and abbots and reserved the custom of requiring them to come and do homage for the " temporalities " ( the landed properties tied to the episcopate ), directly from his hand, after the bishop had sworn homage and feudal vassalage in the ceremony called commendatio, the commendation ceremony, like any secular vassal.

The other vector bundles of tensors have comparable cocycles, which come from applying functorial properties of tensor constructions to the chain rule itself ; this is why they also are intrinsic ( read, ' natural ') concepts.

Its several properties, including the tradeoff between harvesting it and the damage that it does to infantry that come in contact with it, make game strategy more complex for players.

The WJC does not seek any form of commission or gratification payments from Holocaust-era compensation or restitution agreements .” WJC leaders have in particular urged the Polish government to come up with a restitution law for looted private properties, but Warsaw in March 2011 announced that this was impossible due to the current economic situation.

For example, the object and properties of ' a walnut tree ' are joined by the sounds or letters that signify ' walnut tree ' to give us the sign for ' walnut tree ', a set of sounds and written letters that, although they are only arbitrarily connected to a walnut tree, come to mean the ' walnut tree ' to us.

Seedless grape varieties were developed to appeal to consumers, but researchers are now discovering that many of the healthful properties of grapes may actually come from the seeds themselves, thanks to their enriched phytochemical content.

The well water has healing properties and many people come to seek it out.

Its warming properties come from the tiny scales that are on the hollow air-filled fibres.

* In 2009, Marvel attempted to hire a team of writers to help come up with creative ways to launch its lesser-known properties, such as Black Panther, Cable, Iron Fist, Nighthawk, and Vision.

The most active preparations obtained by these two groups of investigators appear to be similar in potency, composition and physical properties.

Even after leaving the abbacy of Tavistock, he continued to hold two properties from the abbey until his death.

As Apollo 16 was the penultimate mission in the Apollo program and there was no new hardware or procedures to test on the lunar surface, the last two missions ( the other being Apollo 17 ) presented opportunities for astronauts to clear up some uncertainties in understanding the Moon's properties.

Most subsequent abeyances ( only a few dozen cases ) were settled after a few years, in favour of the holder of the family properties ; there were two periods in which long-abeyant peerages ( in some cases peerages of doubtful reality ) were brought back: between 1838 and 1841 and between 1909 and 1921.

These two isomers of butene are slightly different in their chemical and physical properties.

Critics also question how any two given properties are determined to be properties of the same object if there is no substance in which they both inhere.

* James ` s Theorem For a Banach space the following two properties are equivalent:

Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to classical ( i. e. non-quantum ) mechanics.

An object thus has two types of properties, intrinsic ( physical ) and objective ( observer specific )

In 860, an attack was made on the city by a new principality set up a few years earlier at Kiev by Askold and Dir, two Varangian chiefs: Two hundred small vessels passed through the Bosporus and plundered the monasteries and other properties on the suburban Prince's Islands.

such that the following two properties hold:

His original system consisted of the four classical elements found in the ancient Greek traditions ( air, earth, fire and water ), in addition to two philosophical elements: sulphur, ‘ the stone which burns ’, which characterized the principle of combustibility, and mercury, which contained the idealized principle of metallic properties.

The mechanism of transformation is structural mapping, in which properties of two or more source domains are selectively mapped onto a blended space ( Fauconnier & Turner, 1995 ; see conceptual blending ).

Now, due to physical properties of interference, if two signals at a point are in phase, they add to give twice the amplitude of each signal, but if they are out of phase, they subtract and give a signal that is the difference of the amplitudes.

A C *- algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties:

Quantitative symbols give a visual measure of the relative size / importance / number that a symbol represents and to symbolize this data on a map, there are two major classes of symbols used for portraying quantitative properties.

This correlation, together with the differences in colour, support further the suggestion that the currently observed classical objects belong to at least two different overlapping populations, with different physical properties and orbital history.

Both ' bitheism ' and ' ditheism ' imply a belief in two equally powerful gods with complementary or antonymous properties.

In physics, dualism refers to mediums with properties that can be associated with the mechanics of two different phenomena.

Many other two-terminal nonlinear devices exist, for example a neon lamp has two terminals in a glass envelope and has interesting and useful nonlinear properties.

These two properties determine whether a given index is worth the cost.

These two properties determine whether a given index is worth the cost.

The formulas relating those two with all other properties are:

The choice above, however, is typical because it has two useful properties.