Re: [ontolog-forum] [ontology-summit] Estimating number of all known fac

[Simon Spero <sesuncedu@xxxxxxxxx>]

On Thu, May 24, 2012 at 3:55 PM, Ed Barkmeyer <edbark@xxxxxxxx> wrote:

Are they not countable?

If you mean "bounded", I doubt it.  If you mean "countable" in the Cauchy sense -- they can be algorithmically placed in 1-to-1 correspondence with the natural numbers -- I won't hazard a guess.

The power set of reals is uncountable; if it counts as known fact that something is a member of that set then the number of known facts we can derive is uncountable.  

One possible approach to making a WAG would be to take a random sample of entries from an encyclopedia and convert them to a logical form.  Only add new entries to your fact base if they aren't already implied by facts from other entries.    Make a guess at a forumula for estimating the number of new facts for entry n+1, find the integral then use it to  guess how many facts are in all entries.  It's not always  algorithmically possible to  tell if a fact is implied by existing facts, but since this is a WAG, you can just put a time or depth limit. 

Simon

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