On Thu, Jan 23, 2014 at 5:39 PM, Sergio Donal <[email protected]> wrote:
> What do you mean by "holes"? > Holes = variables, which are taken to be universally quantified. For example, father(john, peter) is a "ground" sentence (ie, proposition) without holes. But father(X, Y) has 2 holes which can be filled with "objects". If we say ∀ X,Y. father(X, Y) → has_beard(X) then the formula is universally quantified. Such a rule can be "instantiated" by various objects to become ground sentences. So a rule is like a template. One idea is to represent rules in an *ordered* vector space, such that a rule r "covers" an instantiated formula f, if r > f. Such a relation creates a *cone* shape in the vector space. See, for example, the book "Cones and duality" (Aliprantis & Tourky 2007). ------------------------------------------- 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
