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intransitive

 
Dictionary: in·tran·si·tive   (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.

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WordNet: intransitive
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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
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In mathematics, the term intransitivity is used for related, but different, properties of binary relations:

Contents

The property of not being transitive

A relation is transitive if, whenever it relates some A to some B, and that B to some C, it also relates that A to that C. Some authors call a relation intransitive if it is not transitive, i.e.

\neg\forall a, b, c: a R b \wedge b R c \Rightarrow a R c.

Where R indicates some relationship.

For instance, 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, in this sense.

Another example that does not involve preference loops arises in freemasonry: lodge A recognizes lodge B, and lodge B recognizes lodge C, but lodge A does not recognize lodge C. Thus the recognition relation among Masonic lodges is intransitive.

The property of being antitransitive

Often the term intransitive is used to refer to the stronger property of antitransitivity.

We just saw that the eat relation is not transitive, but it still contains some transitivity: for instance: humans eat rabbits, rabbits eat carrots, and human also eat carrots.

A relation is antitransitive if this never occurs at all, i.e.,

\forall a, b, c: a R b \wedge b R c \Rightarrow \neg a R c

Many authors use the term intransitivity to mean antitransitivity.[1][2]

An example of an antitransitive relation: the defeated relation in knockout tournaments. If player A defeated player B and player B defeated player C, A can have never played C, and therefore, A has not defeated C.

A cycle in a binary relation

The term intransitivity is often used when speaking of scenarios in which a relation describes the relative preferences between pairs of options, and weighing several options produces a "loop" of preference:

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

A well-known example is the game rock, paper, scissors.

Assuming no option is preferred to itself, a preference relation with a loop is not transitive. For if it is, each option in the loop is preferred to each option, including itself. This can be illustrated for this example of a loop among A, B, and C. Assume the relation is transitive. Then, since A is preferred to B and B is preferred to C, also A is preferred to C. But then, since C is preferred to A, also A is preferred to A.

Therefore such a preference loop (or "cycle") is known as an intransitivity.

This is not the same property as the relation not being transitive, nor is it the same as the relation being antitransitive.

Occurrences of intransitivity in preferences

  • Analogously, in economics intransitivity can occur in a consumer's preferences. This may lead to consumer behaviour that does not conform to perfect economic rationality. In recent years, economists and philosophers have questioned whether violations of transitivity must necessarily lead to 'irrational behaviour' (see Anand (1993)).

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 conservatism

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. ^ Guide to Logic, Relations II
  2. ^ IntransitiveRelation

See also Anand P (1993) Foundations of Rational Choice Under Risk, Oxford, Oxford University Press


Translations: Intransitive
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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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Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. 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 Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Intransitivity" Read more
Translations. Copyright © 2007, WizCom Technologies Ltd. All rights reserved.  Read more