I have a conjecture that given a particular (multi)set of words without knowledge of ordering, then one ordering is normally much more likely than any others.
- Its not always true,
- Show me flights from Paris to New York." is just as reasonable as "Show me flights from New York to Paris"; and just as likely to occur in real world use.
- On the other hand often one ordering is far more likely and reasonable than the others,
- "The dog chased the cat." is much more often correct than "The cat chased the dog.", it is also preferable over "The cat the dog chased."
- though all three are grammatical.
- Indeed the sentence "The cat chased the dog." may in-fact be the correct sentence (My old neighbor had a cat like that), but how often does it occur? Maybe 1 time in 1000?
- so perhaps it is true for 90% (for example) of sentences.
Fundamentally the question comes down to given a Bag of Words, how often can a good stochastic language model order them correctly (back to the reference the bag came from.).
I'm looking for a reference based on corpus statistics. (My own results suggest it is true for the Brown corpus, though I'ld much rather cite an existing well-known work)
I'm primarily interested in English, though a contrastive notes with more or less strict word-ordering languages would be very interesting.