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Consider the phrase

A transformation rule is a matrix, where certain elements can be accessed by a common name

"Common" can be interpreted in two different, both semantically correct ways

  1. Common in the sense that the name is frequent.

    Emily is a common name according to http://www.studentsoftheworld.info/penpals/stats.php3?Pays=GBR

  2. It can also mean that more than one object shares the same characteristics

    12 and 8 has 4 as a common denominator

How shall I distinguish case (1) from case (2). Is there a way to reformulate the phrase to unambiguously make it like in case (2).

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The preposition to will come to your aid.

A transformation rule is a matrix, where certain elements can be accessed by a name common to (the things you have in mind)

From Oxford (sense 2):

Shared by, coming from, or done by two or more people, groups, or things:

the two republics' common border

problems common to both communities

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  • That does disambiguate the adjective, provided the writer intended it to be read that way, which they probly did. Though it doesn't distinguish the two cases when they aren't disambiguated. – John Lawler May 2 '15 at 14:38
  • @JohnLawler: You're quite right, Sir. I only answered the 2nd part Is there a way to reformulate the phrase to unambiguously make it like in case (2) Hoping someone will answer the first part. Maybe you could help with that. – Tushar Raj May 2 '15 at 14:41

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