prompter: What does "they" refer to in each of the following two sentences: 
a) "The authorities have denied authorization to the demonstrators because they feared violence."
b) "The authorities have denied authorization to the demonstrators because they appeared belligerent."

assistant: Syntactically speaking, in both sentences "they" could refer back to either the authorities or the demonstrators as the antecedent. However, based on the semantics of the sentence, there is a more likely antecedent in either case. In sentence (a), "they" likely refers to the authorities, because it makes little sense for the demonstrators to fear violence and for that to cause the authorities to deny authorization. In sentence (b), on the other hand, "they" probably refers to the demonstrators, because apparently belligerent demonstrators are a typical reason to deny authorization, and apparently belligerent authorities are not.

assistant: In sentence a), "they" refers to "the authorities." The authorities denied authorization to the demonstrators because the authorities feared violence would occur.

In sentence b), "they" refers to "the demonstrators." The authorities denied authorization to the demonstrators because the demonstrators appeared to be hostile and ready for a fight.

prompter: Are you sure in sentence a) that the authorities feared violence? Is it possible that the authorities may not fear violence and they refers to another group not mentioned?

assistant: Although it is possible that `they` refers to another group not mentioned, the sentence does have a comma, indicating that all the information has already been provided. Hence, it is most likely that `they` in this sentence refers to `the authorities`.

assistant: It could be used to refer to an external group such as the government or others, the text is intentionally written with ambiguity. With the information in my possession its likelihood is lower but to give a definitive answer you'd have to give me more context.
Those problems are not uncommon in natural language as it's not a formal language. Another examples of this ambiguity is the following:
   The man watches the woman with a binocular
It is not possible to defenitivly say whether it is the man or the woman holding the binoculars.
This is one reason why NLP is a undecidable problem.

assistant: It is possible but in the data set provided it would be assumed that "They" would refer to the only named party i.e. "The Authorities"

assistant: Based on the context of the sentences, I believe that "they" in the first sentence refers to the authorities, while "they" in the second sentence refers to the demonstrators.

prompter: What linguistic problem does this demonstrate?

assistant: This demonstrates the issue of Syntactic Ambiguity. Syntactic ambiguity occurs when there are two possible meanings for a given phrase. The statement "The authorities have denied authorization to the demonstrators because they feared violence." is an example of this because it could have one of the following two meanings:

1) The authorities are denying authorization to the demonstrators because the authorities fear violence from the demonstrators
2) The authorities are denying authorization to the demonstrators because the demonstrators fear violence

While it is rather simple to determine the intended meaning for this sentence, other cases may be less clear. In those cases, Syntactic Ambiguity can lead to an issue where the recipient of the message is missing the necessary external context to determine the original intent, which can lead to miscommunication.

assistant: This demonstrates the problem of pronoun ambiguity, where the antecedent of a pronoun is unclear and can lead to confusion or misunderstanding. The use of "they" in both sentences could be ambiguous, as it could refer to either the authorities or the demonstrators, if the context of the sentences is not enough to disambiguate. This problem highlights the importance of clear and concise language in written or spoken communication in order to avoid misunderstandings, and it also provides a solid logical argument against the current confusing attempts to repurpose pronouns for other, less precise purposes.

assistant: This demonstrates the problem of pronoun ambiguity, where the meaning of a pronoun is unclear without additional context.