Crossword clues for completeness
The Collaborative International Dictionary
Completeness \Com*plete"ness\, n. The state of being complete.
Wiktionary
n. 1 the state or condition of being complete 2 (context logic English) The property of a logical theory that whenever a wff is valid then it must also be a theorem. Symbolically, letting ''T'' represent a theory within logic ''L'', this can be represented as the property that whenever is true, then must also be true, for any wff ''φ'' of logic ''L''.
WordNet
n. the state of being complete and entire; having everything that is needed [ant: incompleteness]
(logic) an attribute of a logical system that is so constituted that a contradiction arises if any proposition is introduced that cannot be derived from the axioms of the system
Wikipedia
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 estimated on the basis of the statistic: it ensures that the distributions corresponding to different values of the parameters are distinct.
It is closely related to the idea of identifiability, but in statistical theory it is often found as a condition imposed on a sufficient statistic from which certain optimality results are derived.
In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset). The most familiar example is the completeness of the real numbers. A special use of the term refers to complete partial orders or complete lattices. However, many other interesting notions of completeness exist.
The motivation for considering completeness properties derives from the great importance of suprema (least upper bounds, joins, " ∨ ") and infima (greatest lower bounds, meets, " ∧ ") to the theory of partial orders. Finding a supremum means to single out one distinguished least element from the set of upper bounds. On the one hand, these special elements often embody certain concrete properties that are interesting for the given application (such as being the least common multiple of a set of numbers or the union of a collection of sets). On the other hand, the knowledge that certain types of subsets are guaranteed to have suprema or infima enables us to consider the computation of these elements as total operations on a partially ordered set. For this reason, posets with certain completeness properties can often be described as algebraic structures of a certain kind. In addition, studying the properties of the newly obtained operations yields further interesting subjects.
In cryptography, a boolean function is said to be complete if the value of each output bit depends on all input bits.
This is a desirable property to have in an encryption cipher, so that if one bit of the input ( plaintext) is changed, every bit of the output ( ciphertext) has an average of 50% probability of changing. The easiest way to show why this is good is the following: consider that if we changed our 8-byte plaintext's last byte, it would only have any effect on the 8th byte of the ciphertext. This would mean that if the attacker guessed 256 different plaintext-ciphertext pairs, he would always know the last byte of every 8byte sequence we send (effectively 12.5% of all our data). Finding out 256 plaintext-ciphertext pairs is not hard at all in the internet world, given that standard protocols are used, and standard protocols have standard headers and commands (e.g. "get", "put", "mail from:", etc.) which the attacker can safely guess. On the other hand, if our cipher has this property (and is generally secure in other ways, too), the attacker would need to collect 2 (~10) plaintext-ciphertext pairs to crack the cipher in this way.
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 base complete with the closed world assumption - that is, adding all not-entailed literals as negations to the knowledge base. In the above example though, this would not work because it would make the knowledge base inconsistent:
KB' = { A ∨ B, ¬A, ¬B }
In the case you have KB := { P(a), Q(a), Q(b) }, you have KB ⊭ P(b) and KB ⊭ ¬P(b), so with the closed world assumption you would get KB' = { P(a), ¬P(b), Q(a), Q(b) } where you have KB' ⊨ ¬P(b).
See also:
- Vivid knowledge
Category:Knowledge representation
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete. The term "complete" is also used without qualification, with differing meanings depending on the context, mostly referring to the property of semantical validity. Intuitively, a system is called complete in this particular sense, if it can derive every formula that is true. Kurt Gödel, Leon Henkin, and Emil Leon Post all published proofs of completeness. (See History of the Church–Turing thesis.)
Usage examples of "completeness".
The completeness of it is a little surprising, because laboratory tests of planarian worms have established that conditioned reflexes carry over into the new growth.
I twitted her as I pushed myself back till I was crammed inside her to the very hilt, wanting that luxuriating completeness of being thoroughly and fully housed inside her warm narrow quivering grotto.
It is probable that, at the time, the Vendean general had no idea of the completeness of the victory that he had won, or of the disorganization of the enemy.
These payments were to be so made that the integrity, completeness, and success of the work would be their main condition.
That the chance was not delusive was sufficiently guaranteed by the completeness with which he could finally figure it out that, in case of his taking action, neither Ida nor Beale, whose book, on each side, it would only too well suit, would make any sort of row.
It achieves a great deal of completeness at the cost of being inconsistent or incoherent or uncertain, of having no tightly knit unifying regime or common principle.
As its concept, however, such as it is given, may contain many obscure representations which we pass by in our analysis, although we use them always in the practical application of the concept, the completeness of the analysis of my concept must always remain doubtful, and can only be rendered probable by means of apt examples, although never apodictically certain.
What we really insist on is this, that philosophical definitions are possible only as expositions of given concepts, mathematical definitions as constructions of concepts, originally framed by ourselves, the former therefore analytically (where completeness is never apodictically certain), the latter synthetically.
As a whole/part, there is thus a constant tension between coherency or consistency, on the one hand, and completeness, on the other.
Meanwhile, this most learned man confesses, as his opinion that the soul of the world and its parts are the true gods, from which we perceive that his theology (to wit, that same natural theology to which he pays great regard) has been able, in its completeness, to extend itself even to the nature of the rational soul.
The sight of these presents mollified the chieftain, who had, doubtless, been previously rendered considerate by the resolute conduct of the white men, the judicious disposition of their little armament, the completeness of their equipments, and the compact array of battle which they presented.
Its course showed that it was circling around Pertane, possibly checking the completeness of military positions.
Burkett wanted to impress the research director with the completeness of his investigation, but Nachman wasn’.
On many worlds it is well known, though on others the information is suppressed, that biological realities exist, such as dominance and submission, strength and vulnerability, reciprocal needs, jealousy, possessiveness, protectiveness, sexual dimorphism and its meaning, claimancy and command, behavioral genetics, readinesses to respond to sign stimuli, longings for completeness, the desire to belong to, and yield to, the master animal, and such.
For the sake of completeness, I must also mention a third preposterous fable, according to which my grandfather floated out to sea like a piece of driftwood and was promptly fished out of the water by some fishermen from Bohnsack who, once outside the three-mile limit, handed him over to a Swedish deep-sea fisherman.