On Wed, Apr 23, 2014 at 5:40 PM, Anastasios Tsiolakidis <[email protected]>wrote:
> Well, correct me if I am wrong, but I should be looking for the simplest > "logics", right? As semantics etc should be handled in other parts of the > AGI softosphere, in my book at least. > > I was alerted earlier this month to the fact (I haven't entirely verified > it yet), that the GGP general game playing language GDL does not allow for > rules that include past states, so even the chess implementations (the ones > I could find at least) did not include en passant and castling (as chess > players know you may be prohibited from castling in move 200 just because > you moved your king in move 5). Now, I cannot afford any logic with such > blatant flaws, but prop calculus is surely enough, or ...? Still, it is > quite obvious that people have been building on top of and inside Prolog, > and I am kinda out of touch with the reasons why (!) > The logic does not impose any restriction on whether you can represent time or not. But the logic does impose some "expressiveness" constraints. For example, if you want to use time as a variable, as in "castled(t_5)", ie, castled at time step = 5, then this is beyond the expressive power of propositional logic. But you could still employ a propositional logic engine to reason about those problems, if encoded correctly. Propositional logic does not allow any structure *within* propositions. So you have to somehow encode that information into various propositions, then call the inference engine. As a general rule, the more expressive a logic, the slower the inference engine. So this is a trade-off situation, unless some breakthrough happens in inference algorithms. For AGI, it tends to require fairly expressive logics, but then the encoding into propositional logic will blow up exponentially. There was an error in my previous post: when boolean logic is relaxed into interval probabilistic logic, the number of logic formulas blow up exponentially (at least in a naive implementation). So apparently it does not resolve the P!=NP issue. But I will think about this problem deeper... =) ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
