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completeness theorem

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  • Gödel's completeness theorem — is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first order logic. It was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… …   Wikipedia

  • Original proof of Gödel's completeness theorem — The proof of Gödel s completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a rewritten version of the dissertation, published as an article in 1930) is not easy to read today; it uses concepts and formalism that are… …   Wikipedia

  • Completeness — In general, an object is complete if nothing needs to be added to it. This notion is made more specific in various fields. Contents 1 Logical completeness 2 Mathematical completeness 3 Computing 4 …   Wikipedia

  • Theorem — The Pythagorean theorem has at least 370 known proofs[1] In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements …   Wikipedia

  • Completeness of the real numbers — Intuitively, completeness implies that there are not any “gaps” (in Dedekind s terminology) or “missing points” in the real number line. This contrasts with the rational numbers, whose corresponding number line has a “gap” at each irrational… …   Wikipedia

  • Completeness (statistics) — In statistics, completeness is a property of a statistic in relation to a model for a set of observed data. In essence, it is a condition which ensures that the parameters of the probability distribution representing the model can all be… …   Wikipedia

  • Completeness of atomic initial sequents — In sequent calculus, the completeness of atomic initial sequents states that initial sequents A ⊢ A (where A is an arbitrary formula) can be derived from only atomic initial sequents p ⊢ p (where p is an atomic formula). This theorem plays a role …   Wikipedia

  • completeness — Intuitively, a logical system is complete if everything that we want can be derived in it. Thus a formalization of logic is complete if all logically valid forms of argument are derivable in the system; a system designed to codify mathematical… …   Philosophy dictionary

  • completeness — See completely. * * * Concept of the adequacy of a formal system that is employed both in proof theory and in model theory (see logic). In proof theory, a formal system is said to be syntactically complete if and only if every closed sentence in… …   Universalium

  • Completeness (knowledge bases) — A knowledge base KB is complete if there is no formular α such that KB ⊭ α and KB ⊭ ¬α. Example of knowledge base with incomplete knowledge: KB := { A ∨ B } Then we have KB ⊭ A and KB ⊭ ¬A. In some cases, you can make a consistent knowledge… …   Wikipedia

  • Turing completeness — For the usage of this term in the theory of relative computability by oracle machines, see Turing reduction. In computability theory, a system of data manipulation rules (such as an instruction set, a programming language, or a cellular… …   Wikipedia

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