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.

For example, in an axiomatic system, proof of soundness amounts to verifying the validity of the axioms and that the rules of inference preserve validity ( or the weaker property, truth ).

Strong soundness of a deductive system is the property that any sentence P of the language upon which the deductive system is based that is derivable from a set Γ of sentences of that language is also a logical consequence of that set, in the sense that any model that makes all members of Γ true will also make P true.

The converse of the soundness property is the semantic completeness property.

Rather, a foreign decision that is obeyed on the basis of the soundness of its reasoning will be called persuasive authority — indicating that its effect is limited to the persuasiveness of the reasons it provides.

TRAC provides tools for the audit, assessment, and potential certification of digital repositories, establishes the documentation requirements required for audit, delineates a process for certification, and establishes appropriate methodologies for determining the soundness and sustainability of digital repositories.

There is also the problem of " verifying the verifier "; if the program which aids in the verification is itself unproven, there may be reason to doubt the soundness of the produced results.

Such lives are characterized by clarity of thought and expression, the ability to reason, a sense of history and a global perspective, an understanding of literature and language, a knowledge of mathematics and science, an appreciation of the arts, an awareness of political and social realities, a familiarity with the biblical tradition and an ethical awareness, a respect for physical soundness, and an understanding of technology.

The success or failure of a belligerent's efforts to gain air supremacy hinges on several factors including the skill of its pilots, the tactical soundness of its doctrine for deploying its fighters and the numbers and performance of those fighters.

But the state of being falsifiable or scientific says nothing about its truth, soundness or validity, for example the unfalsifiable statement " That sunset is beautiful.

Then, once this claim ( expressed in the previous sentence ) is proved, it will suffice to prove " φ is either refutable or satisfiable " only for φ's belonging to the class C. Note also that if φ is provably equivalent to ψ ( i. e., ( φ ≡ ψ ) is provable ), then it is indeed the case that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable " ( the soundness theorem is needed to show this ).

Granite is one of the rocks most prized by climbers, for its steepness, soundness, crack systems, and friction.

Countless generations of domestic horses bred for size, color, speed, and many other traits with little regard for hoof quality and soundness make some breeds more dependent on horseshoes than feral horses such as mustangs, which develop strong hooves as a matter of natural selection.

The process may involve causal relationships between intermediate events, but in any case the slippery slope schema depends for its soundness on the validity of some analogue for the physical principle of momentum.

Informally, a soundness theorem for a deductive system expresses that all provable sentences are true.

In logic, semantic completeness is the converse of soundness for formal systems.

He was looking for relations of dependence which characterise necessary inference, and distinguished the validity of these relations, from the truth of the premises ( the soundness of the argument ).

Built in 1953, the experimental Bell XV-3 flew until 1966, proving the fundamental soundness of the tiltrotor concept and gathering data about technical improvements needed for future designs.

The Roman Senate responded to the tragedy by banning people with a fortune of less than 400, 000 sesterces from hosting gladiator shows, and also requiring that all amphitheatres to be built in the future be erected on a sound foundation, inspected and certified for soundness.

Edward Foss wrote that he was an " eminent judge, whom all look up to as one of the brightest luminaries of the law, as well for the soundness of his learning as for the excellence of his life ".

The FDIC also examines and supervises certain financial institutions for safety and soundness, performs certain consumer-protection functions, and manages banks in receiverships ( failed banks ).

# Depository institutions possess enormous financial power, by virtue of their control of other people ’ s money ; its extent must be limited to ensure soundness and competition in the market for funds, whether loans or investments.

Laurence Kotlikoff ’ s “ limited purpose banking ” proposal rejects bank regulation ( based on rules and supervision to ensure “ safety and soundness ”) and replaces it with a prohibition on any company operating like a traditional “ bank .” All limited liability financial companies ( not only today ’ s “ banks ”) that receive money from the public for investment or “ lending ” and that issue promises to pay amounts in the future ( whether as insurance companies, hedge funds, securities firms, or otherwise ) could only issue obligations to repay amounts equal to the value of their assets.

The World Series between the Giants and Oakland Athletics was subsequently delayed for 10 days, in part to give engineers time to check the stadium's ( and that of nearby Oakland-Alameda County Coliseum ) overall structural soundness.

The ITA awarded franchises to applicant companies, selecting between applicants on the basis of the financial soundness of the company, the proposals for the service to be offered, and often on connections between the applicant company and the area to be served.

:: SECOND SERIES: To acquaint the reader with the material required for a new creation and to prove the soundness and good quality of it.

The most famous tenor of his generation, he was renowned internationally for the great beauty of his voice and the soundness of his vocal technique.

:: SECOND SERIES: To acquaint the reader with the material required for a new creation and to prove the soundness and good quality of it.

This is an immediate consequence of the completeness theorem, because only a finite number of axioms from Γ can be mentioned in a formal deduction of φ, and the soundness of the deduction system then implies φ is a logical consequence of this finite set.

* logical soundness

" However, Frank Knight, founder of the Chicago School of Economics, wrote in a scholarly review of the Wootton book: " Let me repeat that the Wootton book is in no logical sense an answer to The Road to Serfdom, whatever may be thought of the cogency of Hayek's argument, or the soundness of his position.

We have found it is possible to design a refined multiprogramming system in such a way that its logical soundness can be proved a priori and that its implementation admits exhaustive testing.

A converse to completeness is soundness, the fact that only logically valid formulas are provable in the deductive system.

A converse to completeness is soundness, the fact that only logically valid formulas are provable in the deductive system.

The soundness of a formal system depends on whether or not all of its theorems are also validities.

For a comprehensive analysis of the energy efficiency and environmental soundness of a power system, one should ideally consider a wider range of factors than strict energy conversion AC-to-DC power efficiency.

A probabilistically checkable proof system with completeness c ( n ) and soundness s ( n ) over alphabet Σ for a decision problem L, where 0 ≤ s ( n ) ≤ c ( n ) ≤ 1, is a randomized oracle Turing Machine V ( the verifier ) that, on input x and oracle access to a string π ∈ Σ < sup >*</ sup > ( the proof ), satisfies the following properties:

One of the major tasks of the CBJ is the supervision of the banking system, so as to ensure its soundness, and protect depositors and shareholders.

The renovation also improved the structural soundness of the facility, and included a state-of-the-art sound system.

* ensures the safety and soundness of the national banking system ;

* The Accounting Task Force ( ATF )-ensures that accounting and auditing standards help promote sound risk management thereby maintaining the safety and soundness of the banking system

But the American people can remain confident in the soundness and the resilience of our financial system.

During his term as Comptroller, Hawke has stressed the importance of the safety and soundness of national banks through such supervisory initiatives as Project Canary ( an “ early warning ” system ) and the “ Supervision in the Future ,” which makes extensive use of technology.

SAMA is the Central Bank of Saudi Arabia, the functions of the SAMA include issuing the national currency, the Saudi Riyal, supervising commercial banks, managing foreign exchange reserves, promoting price and exchange rate stability, and ensuring the growth and soundness of the financial system, operating a number of cross-bank electronic financial systems such as ( SPAN, Tadawul, SARIE, SADAD and MAQASA ).