Formal communication benefits from ambiguity minimization
So what exactly do I mean by formal communication? Well when we think of how human beings communicate with machines it is in a formal language. This formal language requires minimized ambiguity for security analysis (how can we analyze code if we cannot effectively interpret it?). The other problem is that the machines require for example that if... then... else and similar conditional statements are well defined and unambiguous.
Is it possible to show that a grammar is unambiguous?
To show a grammar is unambiguous you have to argue that for each string in the language there is only one derivation tree.. This is how it would be done theoretically speaking.
In computer science, an ambiguous grammar is a context-free grammar for which there exists a string that can have more than one leftmost derivation or parse tree, while an unambiguous grammar is a context-free grammar for which every valid string has a unique leftmost derivation or parse tree. Many languages admit both ambiguous and unambiguous grammars, while some languages admit only ambiguous grammars.
Specifically we know that deterministic context free grammars must be unambiguous. So we know unambiguous grammars exist. It appears the strategy is ambiguity minimization with regard to formal languages (such as computer programming languages).
For computer programming languages, the reference grammar is often ambiguous, due to issues such as the dangling else problem. If present, these ambiguities are generally resolved by adding precedence rules or other context-sensitive parsing rules, so the overall phrase grammar is unambiguous.[citation needed] The set of all parse trees for an ambiguous sentence is called a parse forest.[1]
The parse forest is an important concept to note. All possible parse trees for an ambiguous sentence is called a "parse forest". This concept is key to understanding the strategy of ambiguity minimization. So we can in practice minimize ambiguity and we know for certain that deterministic context free grammars admit an unambiguous grammar but what does that mean? What are the benefits of unambiguous language in general?
A benefit of ambiguity minimization
Simple English is a form of controlled English designed to minimize ambiguity in English. This is important because by using simple English to codify the rules or write the laws it puts it in a language where there is less of a computational expense (in brain power) to process and interpret the statements.
In one of my older blogposts 
Her post highlights the fact that there are different love languages and that we don't all speak the same love language. Ambiguity here is actually not a good thing but the simple fact is when someone speaks about love how do we know they are talking about the same thing? As a result we often seek an agreed upon or formally defined "love concept" where we all agree it's love. This is not trivial to find and as a result a topic like love is not easy to discuss in any serious manner. Unambiguous communication or to be more precise (minimized ambiguity) would allow Alice to discuss with Bob the topic of love in a way where they both know exactly what the other is referring to in terms of behavioral expectations, emotions/feelings, etc.
If Alice agrees to love Bob then Bob has no way to determine what Alice means unless he and she agree on a mutually defined concept of love. This highlights how agreement requires very good communication and how minimizing ambiguity can be beneficial at least in this example.
More details:
Ambiguity minimization makes sense when you are following a principle of computational kindness. That is if Alice would like to reduce the computational burden on Bob then she can reduce or minimize the ambiguity of her sentence. This is because in order for Bob to interpret an ambiguous sentence Bob must in essence sort all possible interpretations of that sentence from most likely interpretation to least likely interpretation, and before he can even sort he must first search in order to find all possible or at least plausible interpretations.
This is very computationally expensive for Bob but very cheap for Alice. Alice knows exactly what she means but Bob has no clue what Alice REALLY means.
A benefit of ambiguity
There are other examples where increasing ambiguity could be beneficial, such as perhaps when the communication is less than formal, or to share a stream of consciousness without turning it into a formal communication. Humor for example rides on ambiguity and a good joke may have multiple layers. Art also leverages ambiguity because it's perhaps meant to be interpreted 20 different ways all to produce a certain desired affect.
Ambiguity allows more meaning to be packed into fewer words. This in a sense is a sort of compression scheme. So if a sentence has multiple possible meanings the levels or meanings are still finite. It's a fixed amount of meanings and so theoretically speaking a search can be conducted. In fact this is what a human being does when interpreting natural language where a sentence can have multiple meanings (they do a search for all possible interpretations of that sentence). The problem with this is that it is computationally expensive as a process at least for the human being to try to figure out all possible interpretations of a sentence.
Lawyers when they do their work are working with a specific knowledge base of common legal sentences and common interpretations known in their profession but the rest of us might see a sentence in lawyer-speak and not really know what it means because we will not know the common interpretations. This is a big problem of course because to form agreements between two parties both parties need to have a common understanding (a kind of knowledge symmetric understandability) allowing them both to interpret roughly the same sentence to mean the same thing.
References
- https://en.wikipedia.org/wiki/Deterministic_context-free_language
- https://en.wikipedia.org/wiki/Ambiguous_grammar
- https://en.wikipedia.org/wiki/Ambiguous_grammar#Recognizing_ambiguous_grammars
- Piantadosi, S. T., Tily, H., & Gibson, E. (2012). The communicative function of ambiguity in language. Cognition, 122(3), 280-291.
- http://news.mit.edu/2012/ambiguity-in-language-0119
- Piantadosi, S. T., Tily, H., & Gibson, E. (2012). The communicative function of ambiguity in language. Cognition, 122(3), 280-291.
- Chantree, F., Nuseibeh, B., De Roeck, A., & Willis, A. (2006, September). Identifying nocuous ambiguities in natural language requirements. In Requirements Engineering, 14th IEEE International Conference (pp. 59-68). IEEE.
- Wasow, T., Perfors, A., & Beaver, D. (2005). The puzzle of ambiguity. Morphology and the web of grammar: Essays in memory of Steven G. Lapointe, 265-282.