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answers:

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There are phonetic level, syntactic level, semantic level, phonological level, acoustic level, linguistic level, language level.

Are there any other levels?

What's the order from the bottom up?

And what are they really about?

+1  A: 

Language admits a lot of diversity, but it also obeys a lot of rules (though often loose ones, with tons of exceptions). So in a particular language, certain sounds are more likely to follow other sounds, certain words are more likely to follow others, and so on. The levels are basically the level of modeling.

Acoustic level is trying to determine which acoustic signals are useful for distinguishing human speech. It tries to answer questions like, "Is this background noise or a speech sound?"

Phonological level is based on what sounds are most likely to combine together when it is trying to reconstruct an acoustic signal into a sequence of phonemes. I think this is essentially the same as the phonetic level.

The language level determines what kind of accent the user has, the dialect, etc.

At the syntactic level, you're looking at which words are likely to appear together based on the syntax of the sentence. This gets rid of words that it would have guessed based on the phonological level but would construct ungrammatical sentences.

The linguistic level as I understand it is more a matter of picking the right word (for example, which homonym our versus hour) based on the context.

At the semantic level, it attempts to model the meaning of the sentence and get rid of things that don't conform to the grammatical relations of verbs and prepositions. For example, the verb disappear takes no direct object, so if there is something in that semantic slot, there probably is an error.

The order will depend on the application really, some of them may be collapsed into each other, some may not be used at all. A conceptual hierarchy that makes sense to me is acoustic < phonological = phonetic < language < syntactic < linguistic < semantic.

ealdent