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Tone sandhi, which should be a postlexical rule, is not supposed to be sensitive to lexical information (which is lexical). How can we explain this?

Take Mandarin as an example, the Mandarin yi sandhi is sensitive to lexical information. The sandhi rule is: 55→35/_51; 55→51/_non-51. However, the yi sandhi takes place only in specific positions: e.g. as a indicator of "number: 1" in quantitative phrases (e.g. yi51 ping35 "a bottle of"). In other places, yi would not go through tone sandhi despite followed by a 51/non-51 tone syllable, e.g. di51 yi55 ping35 "the first bottle".

What might be the possible explaination for this?

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The most important thing to recognize is that the correlation "applies between words" and "refers only to phonetic properties" was refuted very early in the history of Lexical Phonology. One typical LP response is to admit "phrasal allomorphs", as exemplified by Hayes' pre-compiled phonology approach. The short version is that the lexical phonology applies w.r.t. an arbitrary subcategorization frame (which extensionally identifies the triggering context vs. the elsewhere condition), so the morphology creates contextx A and B, the phonology refers to A vs B, then the syntax requires insertion of an A allomorph in the A context. That would be how the distribution "a" vs "an" in English is computed.

Another approach is to divide the post-lexical phonology into two sub-parts, P1 and P2, where P2 is the more-pure kind of phonology and P1 can refer to anything. These are the main work-arounds.

Your description of that Mandarin example isn't detailed enough to establish that this is really lexical. It is possible that a lexeme can enter into many different post-lexical constituents with surrounding words, and then there is also the option of directly referring to the relevant phrasal differences. For instance, a numeral plus a "quantity" would form one kind of phrase, and a numeral plus an ordinary noun forms another. In fact, such a distinction is made in Kongo tone sandhi where "bottle (of)" behaves different when modifying an owner vs. modifying (quantifying) a fluid. As a last resort, one can also invoke the truism that "the number 1 is special", in case your examples are all limited to the behavior of the number "1".

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  • yes I should admit that the example I gave above was not good enough. Let's consider this: in Mandarin, "一位" can be pronounced in 2 ways, yi55wei51 (non-sandhi) "ranking first", or, yi35wei51 (sandhi) "a (person)". The two different pronounciations has different meanings here while sharing the same morpheme.
    – T-Rex
    Jun 29, 2021 at 7:54
  • Still, I think what you said in the first paragraph is suitable for my second example: morphology creats context where non-sandhi and sandhi form should occur (context) and phonology refers to the context. I think syntax is not involved in this case.
    – T-Rex
    Jun 29, 2021 at 8:02

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