> First of all, the *tractability* of your algorithm depends on > heuristics that you design, which are separable from the underlying > probabilistic logic calculus. In your mind, these 2 things may be > mixed up. > > Indefinite probabilities DO NOT imply faster inference. > Domain-specific heuristics do that.
Not all heuristics for inference control are narrowly domain-specific Some may be generally applicable across very broad sets of domains, say across all domains satisfying certain broad mathematical properties such as "similar theorems tend to have similar proofs." So, I agree that indefinite probabilities themselves don't imply faster inference. However, we have some heuristics for (relatively) fast inference control that we believe will apply across any domains satisfying certain broad mathematical properties ... and that won't work with traditional representations of uncertainty.... > Secondly, I have no problem at all, with using your indefinite > probability approach. > > It's a laudable achievement what you've accomplished. > > Thirdly, probabilistic logics -- of *any* flavor -- should > [approximately] subsume binary logic if they are sound. So there is > no reason why your logic is so different that it cannot be expressed > in FOL. Yes of course it can be expressed in FOL ... it can be expressed in Morse Code too, but I don't see a point to it ;-) ... it could also be realized via a mechanical contraption made of TinkerToys ... like Danny Hillis's http://www.ohgizmo.com/wp-content/uploads/2006/12/tinkertoycomputer_1.jpg ;-) > > But are you saying that the same cannot be achieved using FOL? > If you attach indefinite probabilities to FOL propositions, and create indefinite probability formulas corresponding to standard FOL rules, you will have a subset of PLN But you'll have a hard time applying Bayes rule to FOL propositions without being willing to assign probabilities to terms ... and you'll have a hard time applying it to FOL variable expressions without doing something that equates to assigning probabilities to propositions w. unbound variables ... and like I said, I haven't seen any other adequate way of propagating pdf's through quantifiers than the one we use in PLN, though Halpern's book describes a lot of inadequate ways ;-) >> 4) most critically perhaps, using uncertain truth values within inference >> control to help pare down the combinatorial explosion > > Uncertain truth values DO NOT imply faster inference. In fact, they > slow down inference wrt binary logic. > > If your inference algorithm is faster than resolution, and it's sound > (so it subsumes binary logic), then you have found a faster FOL > inference algorithm. But that's not true; what you're doing is > domain-specific heuristics. As noted above, the truth is somewhere inbetween. You can find inference control heuristics that exploit general mathematical properties of domains -- so they don't apply to ALL domains, but nor are they specialized to any particular domain. Evolution is like this in fact -- it's no good at optimizing random fitness functions, but it's good at optimizing fitness functions satisfying certain mathematical properties, regardless of the specific domain they refer to > I think one can do > indefinite probability + FOL + domain-specific heuristics > just as you can do > indefinite probability + term logic + domain-specific heuristics > but it may cost an amount of effort that you're unwilling to pay. well we do both in PLN ... PLN is not a pure term logic... > This is a very sad situation... Oh ... I thought it was funny ... I suppose I'm glad I have a perverse sense of humour ;-D ben ------------------------------------------- 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
