On 6/2/08, Matt Mahoney <[EMAIL PROTECTED]> wrote: > > Can you give an example of something expressed in PLN that > > is very hard or impossible to express in FOL? > > "Mary is probably female" > > Not impossible, as Ben says, just awkward. The problem is that nearly every > statement has uncertain truth value, as well as uncertainty about the degree > of uncertainty.
I have briefly surveyed the research on uncertain reasoning, and found out that no one has a solution to the entire problem. Ben and Pei Wang may be working towards their solutions but a satisfactory one may be difficult to find. Yes, we need uncertainties about uncertainties, ie, 2nd-order probabilities. This can be represented as either probability of probability (Ben's approach), or interval probability. It's hard to say which approach is superior. I guess it doesn't matter that much at this stage. Both problems have been solved by other researchers, but the algorithms are rather complex. The question of how we can justify the values of 2nd-order uncertainty can be solved via machine learning: that is, we prove that the learning algorithm will make the values converge to *consistency*. BTW, there is also a "qualitative" approach which tries to dispense with exact values but this approach is not needed if we use 2nd-order values. Another type of uncertainty is fuzziness and the same situation occurs as in probability -- we need 2nd-order fuzziness. Again, the interval fuzzy logic problem has been solved, with complex algorithms. Step 2 is to combine the above solutions. Step 3 is to find heuristics to approximate step 2, 'cause the exact algorithm would definitely be too inefficient. I suppose one can try to tackle steps 2 and 3 at the same time. I don't really understand NARS or Ben's solution so I have to give them the benefit of the doubt ;) YKY ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=103754539-40ed26 Powered by Listbox: http://www.listbox.com
