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# Difference between Circularity and Transitivity?

Posted on 2006-04-06
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What's the difference between the two properties?  They look identical to me.
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Question by:liahow

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ID: 16396627
According to this:   http://stats.oecd.org/glossary/detail.asp?ID=5519       They are the same.
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ID: 16400323
If my dog had circularity he'd be sniffing his own tail, if he had transitivity he'd be sniffing some other dogs tail.
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ID: 16400717
transitivity sounds more one-way and possibly branching:

trans:  a is to b       b is to c    c is to d    d is to e      d is to f      d is to g            therefore  b is to f

circularity  sounds, well circular   :  a is to b    b is to c    c is to d         therefore d is to a

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ID: 16403051
Hi, grg99 is correct..

I will again consider simpler version of his example..

If a -> b and b -> c, then

A) Circularity: c -> a
B) Transitivity: a -> c

So, the only difference is that the direction of carrying out the operation is interchanged.

Now, consider the example..

If  10 < 20, 20 < 30

Then
A) Circularity: 30 < 10.. which is certainly not true.. and hence, circularity fails
B) Transitivity: 10 < 30.. which is true and hence, transitivity holds

---
Harish
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Accepted Solution

neopolitan earned 2000 total points
ID: 16406598
Meaning differs depending on the context.
-In the general practical statistical terms, they are used interchangeably:
An index number property such that the algebraic product of the price index comparing period j with period i and the price index comparing period k with period j is equal to the price index that compares period k directly with period i.
http://unstats.un.org/unsd/methods/icp/gdp/gdp06_htm.htm

-In grammar: circularity means if if it can generate a derivation tree in which some attribute is circularly defined; transitivity means having two different roles for the same word.
http://www.citebase.org/cgi-bin/fulltext?format=application/pdf&identifier=oai:arXiv.org:math/0208184

-In philosophy:
http://ocw.mit.edu/NR/rdonlyres/Linguistics-and-Philosophy/24-03Spring-2005/F5D2E7CE-C74B-42EF-93B9-336AE081F141/0/l3_persist_prson.pdf
http://prosblogion.ektopos.com/archives/2004/06/alston_on_divin.html

-In neural networks and AI and logical circuits, they tend to be fairly strictly different
http://www.vordenker.de/ics/cbrain.htm
http://72.14.203.104/search?q=cache:oYs69yL69FgJ:www.cs.utah.edu/classes/cs3100-ganesh/handouts/lec1/cs3100book.pdf+circularity,+transitivity,+logic+circuits&hl=en&gl=uk&ct=clnk&cd=9

-Same in statistics(mathematics):
the difference becomes more apparent and can be complicated too. Circularity can be non-transitive.
http://www.smu.edu/statistics/faculty/Schucany%20class/BrownHettmansperger2002.pdf

Circularity: goes in circles, more flexible
Transitivity: rather like one-way traffic, in any direction
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