The questions about boundary conditions we keep encountering betray a more general issue.  Already by this point in the discussion the limits of a purely syntactic approach to language are becoming visible.  It is not that one cannot go a long way by that road in the analysis of a particular language and the study of languages in general but when it comes to understanding the purpose of a language, extending its use in a chosen direction, or designing a language for a particular set of uses, what matters above all are the pragmatic equivalence classes of signs demanded by the application and intended by the designer and not so much the peculiar characters of signs representing the classes of practical meaning.

Any description of a language is bound to have alternative descriptions.  In particular, a formally circumscribed description of a formal language, as any effectively finite description is bound to be, is certain to suggest the equally likely existence and possible utility of other descriptions.  A single formal grammar describes but a single formal language, but any formal language is described by many formal grammars, not all of which afford the same grasp of its structure, provide equivalent comprehensions of its character, or yield interchangeable views of its aspects.  Even with respect to the same formal language, different formal grammars are typically better for different purposes.

Resources

• Cactus Language • Pragmatics
• Survey of Animated Logical Graphs
• Survey of Theme One Program

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