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Challenging questions for short answer format! But there's a pattern with this stuff that's always mostly the same. Specialist logics work great on the happy path, but when you dig into it, they always work because of a bunch of simplifying assumptions that keep us within a zone that's sound/complete/decidable. Roughly speaking GOFAI usually "solves" the frame problem only to the extent it accepts hard limits on the domain of discourse, which trade has bad consequences for expressiveness and/or the ability to update things like axioms and beliefs. We tolerate this because if we don't then we're off the happy path and basically doomed. Then time passes, we forget that we agreed to tradeoffs and float the idea of possible generalizing/taming/adapting ;) Not expert enough on SL to really connect the dots, and it's complicated by the fact that the BI family is a weird place that is in some sense neither monotonic nor non-monotonic. Two main issues though. The first is the applicability thing, because lots of stuff just will not allow clean partitions anyway (back to causal and ramifications). Even in the restricted domain of program-logic, if we're talking side-effects and outside the world of theorem provers or something, the real domain is causal logic anyway, plus all the irreducible difficulties of distributed consensus, etc. The second issue is the partition itself, which is fine if you bring it with you, but it has to be discovered otherwise. For problems of unknown structure, I'm guessing that immediately puts you in the position of looking at the exploding space of all possible partitions. Adding an algebraic operator makes for very clean notation but in practice you can't just wave away how difficult that actually is, if it's even decidable in general (and I'm guessing it's not). Turing/Godel/Tarski will all have their due.. so back to the argument for hybrid systems. Heuristics can prune a search space, but what can't be decided ultimately needs some kind of intuition. Which isn't to say that we don't need all kinds of sophisticated heuristics and backtracking and the rest, but just that we need everything we can get for hard problems. Another way of looking at it, GOFAI and new-wave AI are both pretty bad at generalizing but since this happens in ways that are sort of complementary, we can get a lot of leverage by combining them. |