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In a paper I am writing (APA style), I have a sentence like this:

Another category of common sounds found across many languages are the palato-alveolar consonants (~siblants). These include...

The meaning I want to convey is that palato-alveolar consonants are very related to siblants and I add the word 'siblants' in parentheses for laymen who may not be familiar with the term 'palato-alveolar consonants'. However, I do not want to just say

palato-alveolar consonants (siblants)

because they are not totally identical.

Is the usage of the tilde in this case acceptable in my paper? If not, are there any other ways I can convey this information?

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    I would consider something like (approximately: siblants) or (roughly: siblants). – We oath to creation Apr 30 '18 at 17:41
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    Outside of the math world, I don't know that many people are familiar with the use of ~ to mean "is similar to" or "approximately". In addition, in logic it's used as the negation operator. So I advise against using it outside those narrow fields. – Green Grasso Holm Apr 30 '18 at 19:02
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    Why not use Cf, which means compare? It informs your readers that another, comparable but not identical class exists. – Arm the good guys in America Apr 30 '18 at 20:20
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    If you expect lay people to be reading this, you owe it to them to define palato-alveolar consonants rigorously rather than saying 'they're pretty much like sibilants' (note the spelling). But the tilde is not standard for 'nearly identical to'. – Edwin Ashworth Apr 30 '18 at 21:44
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I don't know the context or why you think this information needs to be included here in that manner, but in general I feel rather strongly that people use parentheses to include unnecessary details far too often and that if the information is important enough to be included, then the writer ought to make the effort to write it into the sentence properly. If it is not important enough to make that much of an effort, then it's not necessary to the sentence, is it.

So, use one or the other of these:

"Another category of common sounds found across many languages are the palato-alveolar consonants."

"Another category of common sounds found across many languages are the palato-alveolar consonants, which are similar to sibilants but have important distinctions."

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I think using a tilde as proposed would be a bit ugly, and potentially confusing.

In engineering or IT contexts, I have often seen ~ before numbers to indicate approximately equal but I’ve never before words. This ties up with Wikipedia’s view:

This symbol (in English) informally means "approximately", "about", or "around", such as "~30 minutes before", meaning "approximately 30 minutes before". It can mean "similar to", including "of the same order of magnitude as", such as: "x ~ y" meaning that x and y are of the same order of magnitude.
- wikipedia

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I'd recommend rephrasing without the symbol. The symbol should be reserved for indicating approximate quantities.

What you are trying to convey is that in languages which distinguish a palato-alveolar from an alveolar place of articulation, the distinction is always in sibilant fricatives and affricates. Note that palato-alveolar is an articulatory term, fricative is a physico-acoustical term, and sibilant is an auditory term. So palato-alveolar and sibilant are names from different sets of terminology. Sibilant can also refer to alveolar consonants, so just use a more precise auditory-based term to get equivalence:

...palateo-alveolar (hushing sibilant) consonants

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