consistencykənˈsɪs tən si

**consistency** (n)

- plural
- consistencies

**consistency**

### English Definitions:

#### consistency, consistence, eubstance, body (noun)

the property of holding together and retaining its shape

"wool has more body than rayon"; "when the dough has enough consistency it is ready to bake"

#### consistency, consistence (noun)

a harmonious uniformity or agreement among things or parts

#### consistency (noun)

logical coherence and accordance with the facts

"a rambling argument that lacked any consistency"

#### consistency (noun)

(logic) an attribute of a logical system that is so constituted that none of the propositions deducible from the axioms contradict one another

#### consistency (Noun)

local coherence

#### consistency (Noun)

correspondence or compatibility

#### consistency (Noun)

reliability or uniformity; the quality of being consistent

#### consistency (Noun)

the degree of viscosity of something

#### consistency (Noun)

Freedom from contradiction; the state of a system of axioms such that none of the propositions deduced from them are mutually contradictory

#### Consistency

In negotiation, consistency, or the consistency principle, refers to a negotiator's strong psychological need to be consistent with prior acts and statements. Dr. Robert Cialdini and his research team have conducted extensive research into what Cialdini refers to as the 'Consistency Principle of Persuasion'. Described in his book Influence Science and Practice, this principle states that people live up to what they have publicly said they will do and what they have written down. So Cialdini encourages us to have others write down their commitments as a route to having others live up to their promises.

#### Consistency

In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if it has a model, i.e., there exists an interpretation under which all formulas in the theory are true. This is the sense used in traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead. The syntactic definition states a theory T {\displaystyle T} is consistent if there is no formula φ {\displaystyle \varphi } such that both φ {\displaystyle \varphi } and its negation ¬ φ {\displaystyle \lnot \varphi } are elements of the set of consequences of T {\displaystyle T} . Let A {\displaystyle A} be a set of closed sentences (informally "axioms") and ⟨ A ⟩ {\displaystyle \langle A\rangle } the set of closed sentences provable from A {\displaystyle A} under some (specified, possibly implicitly) formal deductive system. The set of axioms A {\displaystyle A} is consistent when φ , ¬ φ ∈ ⟨ A ⟩ {\displaystyle \varphi ,\lnot \varphi \in \langle A\rangle } for no formula φ {\displaystyle \varphi } .If there exists a deductive system for which these semantic and syntactic definitions are equivalent for any theory formulated in a particular deductive logic, the logic is called complete. The completeness of the sentential calculus was proved by Paul Bernays in 1918 and Emil Post in 1921, while the completeness of predicate calculus was proved by Kurt Gödel in 1930, and consistency proofs for arithmetics restricted with respect to the induction axiom schema were proved by Ackermann (1924), von Neumann (1927) and Herbrand (1931). Stronger logics, such as second-order logic, are not complete. A consistency proof is a mathematical proof that a particular theory is consistent. The early development of mathematical proof theory was driven by the desire to provide finitary consistency proofs for all of mathematics as part of Hilbert's program. Hilbert's program was strongly impacted by the incompleteness theorems, which showed that sufficiently strong proof theories cannot prove their own consistency (provided that they are in fact consistent). Although consistency can be proved by means of model theory, it is often done in a purely syntactical way, without any need to reference some model of the logic. The cut-elimination (or equivalently the normalization of the underlying calculus if there is one) implies the consistency of the calculus: since there is no cut-free proof of falsity, there is no contradiction in general.

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