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

[Simon Spero <sesuncedu@xxxxxxxxx>]

On Thu, May 24, 2012 at 2:35 PM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:

Adrian,

I think the question about counting facts was more properly a question about identity conditions: Given purported facts f1 and f2, under what conditions is f1 = f2? Given an answer to that question, we then know whether or not we've got one fact or two, i.e., we can know how to count them. It doesn't follow we'll know how many there are (though we might, given a sufficiently well circumscribed domain and a sufficiently rigorous notion of a fact). :-)

Absolutely (well Relatively).   I do think that there must be a rather restricted interpretation of know(n) as well; otherwise to be countable the domain will probably have to be too restricted to be be useful. One would not want  

(know-fact (that (natural-number 0)))

(know-fact (that (forall ?n (if               (natural-number ?n) 

              (natural-number (S ?n)))))

to entail that an infinite number of facts are known. This might be two facts. But we could add the knowledge that nothing else is a natural number, merge the two clauses into a single  formula yet have only one fact.

  (know-fact (that 

         (forall ?n 

          (iff (or (= ?n 0)

   (and (= ?n (S ?n1))

        (know-fact (that (natural-number ?n1)))))

            (know-fact (that (natural-number ?n))))))

Now, it a possible rule that might make sense would be to only count as a known fact ground formula which have been directly asserted by a True Believer™, or which have been generated and cached in some fixed form as a result of answering some question (or pre-computed,etc) .  

So if we have an inference engine with memoization and backward chaining, asking: (natural-number (S (S (S 0))))  might cause us to know 5 facts.  

I really don't like this solution. 

Simon 

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