What do you mean by "holes"?
On Thu, Jan 23, 2014 at 2:42 AM, YKY (Yan King Yin, 甄景贤) < [email protected]> wrote: > There is no royal road... we have to spell out more details: > > 1. Consequence operator can be broken down to single steps: > Cn(F) = lim > n →∞ > , > Stⁿ(F) > > 2. Each single step is the set union of the results of individual rules r > ∈ R: > St(F) = ⋃ r(F) > > 3. A single rule is of the form: > head → tail > and it performs, for all facts f ∈ F: > r(F) = tail * { sub | head * sub = f } > where "x * sub" means substituting sub into formula x. The { | } is set > comprehension. > > The last equation says to find all subs such that head * sub equals a fact > ∈ F. That is unification. > > What remains to do is to find a spatial interpretation of the act of > substitution, *. That depends on how to represent "formulas with holes", > which is predicate logic. For example, "father(X,Y)" is a formula with 2 > holes. > > If we can represent such "predicated" (or "quantified") formulas in space, > then we can spatialize substitution etc... > > More later =) > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/15717384-a248fe41> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > ------------------------------------------- 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
