Parse forest from an ambiguous grammar
To use such a parser, you need some external way to select among the possible trees in the forest.  Typically there are additional constraints beyond what is encoded in the context-free grammar, which can be used to identify the correct parse.  In other words, there are some rules that are part of the syntax (they are part of the context-free grammar, and thus handled by the parser), and some rules that are part of the semantics; there may be multiple parses that are compatable with the syntax rules, and then the semantic rules are used to select which one complies with the semantic rules.