Results for intransitive
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Dictionary:

intransitive

  (ĭn-trăn'sĭ-tĭv, -zĭ-) pronunciation
adj. (Abbr. intr. or int. or i.)

Designating a verb or verb construction that does not require or cannot take a direct object, as snow or sleep.

n.

An intransitive verb.

intransitively in·tran'si·tive·ly adv.
intransitiveness in·tran'si·tive·ness or in·tran'si·tiv'i·ty n.
 
 
WordNet: intransitive
Note: click on a word meaning below to see its connections and related words.

The adjective has one meaning:

Meaning #1: (grammar) designating a verb that does not require or cannot take a direct object
  Antonym: transitive (meaning #1)


 
Wikipedia: intransitivity

In mathematics, intransitivity is the property of a binary relation's not being transitive.

Although the word transitivity is often used very generally when speaking of many sorts of binary relations other than preference orderings, the term intransitivity is seldom used except when speaking of scenarios in which weighing several options produces a "loop" of preference. For example:

  • A is preferred to B
  • B is preferred to C
  • C is preferred to A

A concrete example of intransitivity that does not involve preference loops arises in food chains: wolves eat deer, and deer eat grass, but wolves do not eat grass. Thus the eat relation among life forms is intransitive.

Formal definitions, with examples

There are several different notions of intransitivity.

In mathematics, a binary relation Failed to parse (unknown function\scriptstyle): \scriptstyle R

is transitive if Failed to parse (unknown function\scriptstyle): \scriptstyle\forall a, b, c,\ \left(a R b\ \mathrm{and}\ b R c\right)\ \mathrm{implies}\ a R c.


Examples of transitive relations include "more than", "lives in the same county as", and "is ancestor of".

The transitive closure of a relation is the smallest transitive relation that includes it. For example,

  • "is ancestor of" is the transitive closure of "is parent of"
  • "is connected by road with" is the transitive closure of "is on a road leading to"
  • (for atoms) "is in the same molecule as" is the transitive closure of "has a molecular bond with"

A relation is sometimes called intransitive to indicate that it is not transitive. That is to say, if not for all a, b, c, a R b and b R c implies a R c.

A more common mathematical definition, however, is this: a binary relation R is intransitive (or antitransitive) when Failed to parse (unknown function\scriptstyle): \scriptstyle\forall \{ a, b, c \}((a R b\text{ and }b R c)\implies\text{ not }a R c) . [1] [2]

This notion is stricter: every nonempty relation that is antitransitive, is not transitive, but the reverse does not hold: many relations are neither transitive nor antitransitive.

Antitransitivity does not seem to be a very useful characterization of a relation. Note that it is still possible to have Failed to parse (unknown function\scriptstyle): \scriptstyle\{ a, b, c, d \}

with Failed to parse (unknown function\scriptstyle): \scriptstyle a R b

, Failed to parse (unknown function\scriptstyle): \scriptstyle b R c , Failed to parse (unknown function\scriptstyle): \scriptstyle c R d , and Failed to parse (unknown function\scriptstyle): \scriptstyle a R d .

Examples of antitransitive relations:

  • "is married to"
  • "is parent of", if we disregard incest

The notion mentioned in the first paragraph, however, is different, and can be defined as follows: an intransitivity (or conflict) in a binary relation R is a pair a, b such that a R+ b and b R a, where R+ is the transitive closure of R. A relation has intransitivity if such a pair exists, i.e., if its transitive closure is not antisymmetric. Most mathematicians will not use the term intransitive to describe such a relation, but instead say that it does not define a partial order.

Occurrences

Likelihood of intransitivity

It has been suggested that Condorcet voting tends to eliminate "intransitive loops" when large numbers of voters participate because the overall assessment criteria for voters balances out. For instance, voters may prefer candidates on several different units of measure such as by order of social consciousness or by order of most fiscally conservative.

In such cases intransitivity reduces to a broader equation of numbers of people and the weights of their units of measure in assessing candidates.

Such as:

  • 30% favor 60/40 weighting between social consciousness and fiscal conservatism
  • 50% favor 50/50 weighting between social consciousness and fiscal conservatism
  • 20% favor a 40/60 weighting between social consciousness and fiscal conservatisim

While each voter may not assess the units of measure identically, the trend then becomes a single vector on which the consensus agrees is a preferred balance of candidate criteria.

References

  1. ^ http://www.jgsee.kmutt.ac.th/exell/Logic/Logic42.htm#33
  2. ^ http://www.virtual.cvut.cz/kifb/en/concepts/_intransitive_relation.html

External links


 
Translations: Translations for: Intransitive

Dansk (Danish)
adj. - intransitiv
n. - intransitiv (verbum uden genstandsled)

Nederlands (Dutch)
onovergankelijk, intransitief

Français (French)
adj. - intransitif
n. - intransitif

Deutsch (German)
adj. - intransitiv
n. - (ling.) Intransitiv

Ελληνική (Greek)
adj. - (γραμμ.) αμετάβατος
n. - (γραμμ.) αμετάβατο ρήμα

Italiano (Italian)
intransitivo

Português (Portuguese)
adj., -
n. - intransitivo

Русский (Russian)
непереходный глагол

Español (Spanish)
adj. - intransitivo
n. - modo intransitivo

Svenska (Swedish)
adj. - intransitiv
n. - intransitivt verb

中文(简体) (Chinese (Simplified))
不及物的, 不及物动词

中文(繁體) (Chinese (Traditional))
adj. - 不及物的
n. - 不及物動詞

한국어 (Korean)
adj. - 자동사의, 자동의
n. - 자동사

日本語 (Japanese)
adj. - 自動の, 自動的な
n. - 自動詞

العربيه (Arabic)
‏(صفه) لازم, غير متعد (الاسم) فعل لازم أو غير متعد‏

עברית (Hebrew)
adj. - ‮עומד (פועל)‬
n. - ‮פועל עומד‬


 
 

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Copyrights:

Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved.  Read more
WordNet. WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved.  Read more
Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Intransitivity" Read more
Translations. Copyright © 2007, WizCom Technologies Ltd. All rights reserved.  Read more

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