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I've noticed in some papers (CS) that even if the authors define acronyms in the abstract, they restate them once again in the rest of the paper. It is like "what happens in the abstract stays in the abstract"!

So, I was wondering if there is a rule regarding the above?

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Abstracts are read separately from the paper itself. They aren't an introduction, but more of a condensed version.

So if the paper defines an acronym, it shouldn't rely on the abstract for it. On the other hand, the abstract is supposed to be fairly short, so there isn't usually much of a case for defining acronyms there.

It depends on the paper, of course, but consider spelling out the whole term in the abstract if it is referenced only once there.

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I was wondering if there is a rule regarding the above?

There is a simple rule: always do what is most helpful for your reader. Often your reader will not read the abstract of the paper at the same time as the body, so it would not be unusual for a reader to start reading the paper without first reading the abstract (perhaps having read it at some previous time). If they read from the start of the body, and are presented with acronyms that are not defined, that might lead them to a situation where they don't understand some part of your paper. I would therefore recommend erring on the side of caution and defining your acronyms in the body of the paper.

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I would repeat it. Some people read abstracts only (e.g. Chem Abstracts is a pulication of abstracts). Those who are reading the paper may not read the abstract.

Really, each should be self-supporting. Otherwise, you start to morph the abstract from an abstract to an introduction.

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Usually its convenient, if possible, to include a small glossary in the beginning of the paper. In this way it´s possible to consult every time you came up with an acronym in the text. Also, re-defining them in the text is better. Sometimes readers don´t assume abstract and paper as part of a whole.

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This answer partially repeats what I said here

Abstract are tricky. For example, APA 5 style used to say that abstracts had to be self contained. That meant you had to introduce acronyms in the abstract and then again in the body. In APA 6, this has been dropped (cf. this blog post). I still go with introduce the acronym on first use in the abstract and then again on first use in the body. I also introduce acronyms on first use in figure captions (not sure that is APA style or Strongbad style).

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