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I have published two papers, say A and B. The core of A and B is totally different but they have a similar background.

The similarity of A and B is <1% using iThenticate.

However, I accidentally found that A and B share two sequential almost identical sentences in the introduction of background (totally 40 words). B also cites A but in other place. Is it self-plagiarism?

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    This is quite common (at least the example you gave). You can find sentences duplicated verbatim in different papers by the same author(s) in introduction, background, review of relevant results, etc.
    – Bilbo
    Apr 23, 2022 at 1:00
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    As an aside, using a "plagiarism checker" on your own work in an attempt to determine whether something you wrote constitutes plagiarism makes about the same amount of sense as using a "lie detector" on yourself in an attempt to determine whether something you said constitutes a lie. Apr 23, 2022 at 15:17

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This happens quite often, especially with more general, uncontroversial statements, where you simply run out of possible ways to say the same but with different words. I think a good way of looking at it is that if that sentence says something that someone else might possibly cite you for, then you should also cite yourself. But if it is something trivial, then it is not plagiarism, even if the sentences are almost completely alike. What is the real problem with self-plagiarism? It is not that you repeat yourself now and then. It is that you get double credit for the same work. If the two papers are on completely different topics, this will not happen.

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If one paper cites the other then it is almost certainly fine. Relax. Any reader finding B will also be able to find A making the complete context available.

Without a citation it would depend on what the sentences say. Plagiarism is about ideas and it would probably be hard to capture a complete idea in a couple of sentences in a way that resulted in plagiarism, but it is possible.

Let me emphasize that plagiarism is about the ideas, not the specific words to express them. It is possible to commit plagiarism, including self plagiarism, using none of the original words. For a scholarly paper, self plagiarism occurs when you include ideas that you have published previously without citation, giving the impression that they are new in this paper. It has the effect of cutting off a reader of the current paper from the complete context of the ideas and how they arose.

Also note that most people, when writing about similar things, are likely to use similar phrasing. We tend to fall into patters of language. I'll guess that is all that is happening here.

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