Natural languages necessarily have certain inherent ambiguity. If there were a natural language without inherent ambiguity, then one could have easily adopted such a natural language and used it as a programming language, which would have obviated the need for having to invent a programming language and learning it -- at least for those people who speak the ambiguity-free language. But I've never heard that any ethnic group used their own natural language as a programming language. Which proves the proposition set forth at the outset of this paragraph.
Specifically, I'd like to focus on inherent syntactic ambiguity in natural languages. I was wondering if there is a grammar of syntax that embraces this inherent syntactic ambiguity as an integral part of the grammar. Two most famous grammars that I know of are Constituency Grammar and Dependency Grammar. As far as I know, however, neither of these grammars systematically describes inherent syntactic ambiguity in a natural language.
For example, in "I have a bad feeling about this", "about this" can be viewed as a complement of either "have" or "feeling". Semantically, it doesn't really matter how it is viewed. But syntactically it has to be determined either way. Otherwise, you wouldn't even be able to draw a definite tree diagram out of this sentence, whether according to Constituency Grammar or Dependency Grammar.
Now, I'm no linguist, so I'm not aware of how either of these grammars deals with such syntactic ambiguity or indeterminacy, or even whether either actually does deal with it. So, anyone well aware of these grammars could enlighten me on the 'how' and/or the 'whether' question(s).
If neither deals with such syntactic ambiguity, is there any new approach out there that embraces such syntactic ambiguity and allows you to draw a single tree diagram out of a sentence having syntactic ambiguity?
I feel the need to clarify what I mean by "inherent syntactic ambiguity".
By "inherent syntactic ambiguity" I mean the kind of ambiguity that has a single unambiguous interpretation in terms of semantics and pragmatics that still has ambiguity in terms of syntax.
Thus, a sentence with "inherent syntactic ambiguity" necessarily leads to two or more different tree diagrams under either Constituency or Dependency scheme.
Also, such ambiguity is "inherent" in the sense that no additional context could possibly disambiguate the syntactic ambiguity, as shown in the above "I have a bad feeling about this" example.