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Suppose in some language the following happens:

  • when the stem ends in front vowels (i, e), then adding a certain suffix X requires j insertion (so it looks like [.. i j X] or [... e j X] instead of [... i X] or [... e X])
  • whem the stem ends in back vowels (u, o), then adding the same suffix X requires w insertion (so it looks like [.. u w X] or [... o w X] instead of [... u X] or [... o X])

How to express this in SPE-style notation? I thought about using (in each case, separately) gemination and then "laxing" of the geminate (by laxing I mean [+syllabic] becomes [-syllabic]), but does it really work? Are there more reasonable options?

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There are three subparts to this question. First, the general form of a rule of insertion is Ø→[...]/X__Y. Second, the conditional part of the rule is "w if precede by a back vowel, j if preceded by a front vowel", which is typically expressed using greek-letter variables (αback...αback expands to [+back]...[+back], [-back]...[-back]). Finally, you would need to invoke a feature likes "stem" to say that only a stem vowel causes this (if that is the intent), and you'd have to somehow find a way to describe the suffix X. I don't see any way to treat this as gemination (lengthening) then laxing.

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