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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.

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## Some Related Sentences

Soundness and is

__Soundness__properties come

**in**two main varieties: weak and strong soundness,

**of**

**which**

**the**former

__is__

**a**restricted form

**of**

**the**latter

**.**

*

__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__guarantees

**that**

**all**possible behaviours are preserved while completeness guarantees

**that**no behaviour

__is__added by

**the**encoding

**.**

Soundness and for

* October 1992 – The Housing and Community Development Act

**of**1992 codifies within its**language****the**Federal Housing Enterprises Financial Safety and__Soundness__Act**of**1992**that**creates**the**Office**of**Federal Housing Enterprise Oversight, and mandates HUD to set goals__for__lower income and underserved housing areas__for__**the**GSEs Fannie Mae and Freddie Mac
*

__Soundness__: If x ∉ L then__for__every π, V < sup > π </ sup >( x ) accepts with probability at most s ( n ).

Soundness and .

In Quality

**of**Management they scored second place, third**in**Long Term Investments, fourth**in**Financial__Soundness__, and ninth**in**Global Competitiveness__.__

deductive and system

Certain features we have touched

**upon**: philosophy as**a**logical,__deductive____system__from**which****a**social science methodology can be built up ; ;
Even Plato had difficulties with logic ; although he had

**a**reasonable conception**of****a**__deductive____system__, he could never actually construct one and relied instead**on**his dialectic**.**
Thus, an axiom

**is**an elementary basis**for****a**formal logic__system__**that**together with**the**rules**of**inference define**a**__deductive____system__**.**
A

__deductive____system__consists**of****a**set**of**logical axioms,**a**set**of**non-logical axioms, and**a**set**of**rules**of**inference**.**
Gödel's completeness theorem establishes

**the**completeness**of****a**certain commonly used type**of**__deductive____system__**.**
There

**is**thus,**on****the**one hand,**the**notion**of**completeness**of****a**__deductive____system__and**on****the**other hand**that****of**completeness**of****a**set**of**non-logical axioms**.**
Although many

**of**Euclid's results had been stated by earlier mathematicians, Euclid was**the**first to show how these propositions could fit into**a**comprehensive__deductive__and logical__system__**.**
To formally state, and then prove,

**the**completeness theorem, it**is**necessary to**also**define**a**__deductive____system__**.**
A

__deductive____system__**is**called complete if every logically valid formula**is****the**conclusion**of**some formal deduction, and**the**completeness theorem**for****a**particular__deductive____system__**is****the**theorem**that**it**is**complete**in**this sense**.**
A converse to completeness

**is**soundness,**the**fact**that**only logically valid formulas are**provable****in****the**__deductive____system__**.**
If some specific

__deductive____system__**of**first-order logic**is**sound and complete, then**is**it " perfect " (**a**formula**is****provable**iff it**is****a****semantic**consequence**of****the**axioms ), thus equivalent to**any**other__deductive____system__with**the**same quality (**any**proof**in**one__system__can be converted into**the**other ).
Gödel's completeness theorem says

**that****a**__deductive____system__**of**first-order predicate calculus**is**" complete "**in****the**sense**that**no additional inference rules are required to prove**all****the**logically valid formulas**.**
A converse to completeness

**is**soundness,**the**fact**that**only logically valid formulas are**provable****in****the**__deductive____system__**.**
It

**is**possible to produce sound__deductive__systems**for**higher-order logics, but no such__system__can be complete**.**

deductive and is

However, as to whether inductive

**or**__deductive__reasoning__is__more valuable still remains**a**matter**of**debate, with**the**general conclusion being**that**neither__is__prominent**.**
A brilliant London-based " consulting detective " residing at 221B Baker Street, Holmes

__is__famous**for**his intellectual prowess and__is__renowned**for**his skillful use**of**astute observation,__deductive__reasoning, and forensic skills to solve difficult cases**.**
Popper argued

**that**this would require**the**inference**of****a**general rule from**a**number**of**individual cases,**which**__is__inadmissible**in**__deductive__logic**.**
However, if one finds one single black swan,

__deductive__logic admits**the**conclusion**that****the**statement**that****all**swans are white__is__false**.**

deductive and property

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****.**

deductive and any

In

**a**__deductive__**theory**,__any__**sentence****which****is****a**logical consequence**of**one**or**more**of****the**axioms**is****also****a****sentence****of****that****theory****.**
* as basically

**a**transformation**of****a**__deductive__categorical syllogism ( but**in**1903 he offered**a**variation**on**modus ponens instead, and by 1911 he was unconvinced**that**__any__one form covers**all**hypothetical inference ).
* " Class " as an analytical feature

**of**__any__Category**or**Categorical term,**in****the****language****of**__deductive__reasoning
The term ' syntactic ' has

**a**slightly wider scope than ' proof-theoretic ', since it may be applied to properties**of**formal languages without__any____deductive__systems, as well as to formal systems**.**
Though they require some filling

**in**, enthymemes are intended to have**the**form**of**valid__deductive__syllogisms, so**a**complete enthymeme has**the**same premise-premise-conclusion structure as__any__syllogism, and**is**intended to guarantee**the**truth**of**its conclusion**based****on****the**truth**of**its premises**.**
The structural criterion requires

**that**one who argues**for****or**against**a**position should use an argument**that**meets**the**fundamental structural requirements**of****a**well-formed argument, using premises**that**are compatible with one another,**that**do not contradict**the**conclusion,**that**do not assume**the**truth**of****the**conclusion, and**that**are not involved**in**__any__faulty__deductive__inference**.**
: during

**the**period**of**elaboration**of**__any____deductive__**theory**we choose**the**ideas to be represented by**the**undefined symbols and**the**facts to be stated by**the**unproved propositions ; but, when we begin to formulate**the****theory**, we can imagine**that****the**undefined symbols are completely devoid**of**meaning and**that****the**unproved propositions ( instead**of**stating facts,**that****is**, relations between**the**ideas represented by**the**undefined symbols ) are simply conditions imposed**upon**undefined symbols**.**0.150 seconds.