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This question has been asked before (here is the link phonological ambiguity). In relation to this question, I came across some data in which two different syntactic structures (with the same phonological structure) are polysemous in the sense that the first is encoded in the active voice and the second is encoded in the passive voice.

(1)

Active: X dug a small well

Passive: X dug a small well

X in the active voice refers to the Agent (doer of the action), but it refers to the object in the passive (a small well). The structures in (1) are transliteration of the sentences in (2) below:

(2)

ACTIVE

t.Rza                 t.anu.t

3rd.F.SG.*dig*.PRF   (a small) well
'She has dug a small well.' 

PASSIVE

t.Rza t.anu.t

3rd.F.SG.dig.PRF (a small) well

'A small well has been dug.'

In the literature of Distributed Morphology, Borer (2005a, 2005b, 2013) argues that ONLY words can be polysemous, but not STRUCTURES. I am not sure of any work which considers syntactic structures polysemous in this sense of 'voice syncretism', and I am not sure about their existence in other languages too, if anyone knows more about this issue please tell me. Thank you.

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    To the question: Can there be multiple valid parses? Yes, as in the answer to the question you linked. Can there be multiple valid parses even if POS is held constant for each node? Yes, also. It is often ambiguous where prepositions attach, eg He shot his first goal in February. Sep 6 '18 at 14:52
  • A.M. Bittingmayer, thank you for this answer. Are you aware of any reference discussing this issue?
    – Tsutsu
    Sep 6 '18 at 17:43
  • No, I'm not, I really just approach all of this from the engineering perspective. Engineers who build parsers think about it. (You can try a parsing library and see how it decides.) Manning mentions it, although only the first case as far as I know. And there are the Winograd Schemata and the Winograd Schema Challenge. Sep 6 '18 at 19:42
  • Well, thank you, I'll go through it from another perspective, I'll try delving into systematic polysemy & non-systematic one first, then see works of DMs, and probably use computational approaches as you proposed too.
    – Tsutsu
    Sep 7 '18 at 8:38

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