Partial and Partially Erroneous
Sometime ago, linguist (and political dissident) Noam Chomsky started using the term "Partial and Partially Erroneous" (PAPE) in reference to a native speaker's grasp of the native language. When applied to language, it is a simple concept. Let's start with some of the basics.
Language is an Observable Emergent Behavior (OEB). Intelligent humans of varying levels of intelligence communicate for various reasons, the most common of which is to convey knowledge. To effect this communication, a language is used. This language may take on many forms, but we'll focus on the verbal (oral) and written forms of language. As I write this, I'm demonstrating the use of language. I'm attempting to provide you with knowledge of something that I believe to know. You are attempting to understand the knowledge that I am trying to convey (or getting bored by this). In order for this discourse (transfer through language), we must have a common understanding of the language. Here's the catch: I don't know everything about the English Language. In fact, some of the facts about the English Language that I believe to be correct (in my understanding) may actually be wrong. You also don't know everything about the English Language (if you do, please drop me a line) and it could be argued that you have (in your understanding) at least one incorrect piece of knowledge about the English Language. So how can we possibly share knowledge in the face of these difficulties?
I want to be clear about this concept. Whether I use a prescriptive or descriptive grammar for communications, I use language. I do not use XML, XSD or any other insufficient schema definition. In the language, I have lexical semantics (not axiomatic, operational or denotational), morphology, syntax, phonology and other tools at my disposal. I can communicate the knowledge that I wish to convey to another party with these tools. Again these tools are a partial set where that set may be partially erroneous.
While I'll not provide the supporting mathematics here, the problem of communications in the face of PAPE appears to be at least NP-Complete.