Although a good lexical definition should reduce the ambiguity inherent in a term, it cannot reduce the terms vagueness. For that, we need to move to a precising definition (also sometimes called an explicative definition). Such definitions are similar to lexical definitions in that they are supposed to accurately reflect how a term is used by people generally or at least by a certain community. Precising definitions are also similar to stipulative definitions in that they propose to use a term in a way that is more narrow than usual.
Where precising and stipulative definitions part company is that while stipulative definitions can be completely arbitrary, precising definitions are limited by the context of the more general lexical definition. Whatever a precising definition says, it must already be at least implied or otherwise contained by the full lexical definition. However, unlike the lexical definition, there is no expectation that everyone in every context accept it on the contrary, precising definitions are usually employed for a specific purposes or context.
One example would be in legal circles. In laws we can find all sorts of words which are necessarily vague and that vagueness can hinder a courts ability to apply the law. Thus, courts will use precising definitions according to which a word is said to mean something for the purposes of that law, but not necessarily any other law, let alone general, lexical usage. A good example of this would be the meaning of the word person. Corporations are treated as persons for the purpose of some laws (like those on speech) but not others (like those on voting).
Because precising definitions do propose a usage that isnt common, others arent necessarily obligated to accept them. Thus, as with stipulative definitions, a person can simply reject a precising definition by arguing that it is still too vague, too obscure, or perhaps not related enough to the original term. A certain amount of legal debate involves deciding upon the proper precising definitions to use.
More: What are Definitions?

