Difference between Circularity and Transitivity?

Posted on 2006-04-06
Last Modified: 2013-11-19
What's the difference between the two properties?  They look identical to me.  
Question by:liahow
    LVL 26

    Expert Comment

    According to this:       They are the same.
    LVL 27

    Expert Comment

    If my dog had circularity he'd be sniffing his own tail, if he had transitivity he'd be sniffing some other dogs tail.
    LVL 22

    Expert Comment

    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

    LVL 37

    Expert Comment

    by:Harisha M G
    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

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

    LVL 11

    Accepted Solution

    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.

    -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.

    -In philosophy:

    -In neural networks and AI and logical circuits, they tend to be fairly strictly different,+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.

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

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