On Tuesday 28 November 2006 14:47, Philip Goetz wrote: > The use of predicates for representation, and the use of logic for > reasoning, are separate issues. I think it's pretty clear that > English sentences translate neatly into predicate logic statements, > and that such a transformation is likely a useful first step for any > sentence-understanding process. Whether those predicates are then > used to draw conclusions according to a standard logic system, or are > used as inputs to a completely different process, is a different > matter.
I would beg to differ. While it is clearly straightforward to translate a sencence into a predicate expression in a syntactic way, the resulting structure has no coherent semantics. Consider how much harder it is to translate a sentence of English into a sentence of Chinese. Even then you won't have uncovered the meat of the semantics, since in both languages you can rely on a lot of knowledge the hearer already knows. But when you put the sentence into predicate form, you've moved into a formalism where there is no such semantics behind the representation. In order to provide them, you have to do the equivalent of writing a Prolog program that could make the same predictions, explanations, or replies that a human speaker could to the original English sentence. Consider the following sentences. Could you translate them all using the single predicate on(A,B)? If not, the translation gets messier: On the table is an apple. On Lake Ontario is Toronto. On Hadamard's theory transubstantiation is ineffable. On Comet, on Cupid, on Prancer and Vixen. On Christmas we open presents. On time is better than late. On budget expenditures are dwarfed by Social Security. On and on the list goes... > > The open questions are representation -- I'm leaning towards CSG in > > Hilbert spaces at the moment, but that may be too computationally > > demanding -- and how to form abstractions. > > Does CSG = context-sensitive grammar in this case? How would you use > Hilbert spaces? Sorry -- should have been clearer. Constructive Solid Geometry. Manipulating shapes in high- (possibly infinite-) dimensional spaces. Suppose I want to represent a face as a point in a space. First, represent it as a raster. That is in turn a series of numbers that can be a vector in the space. Same face, higher resolution: more numbers, higher dimensionality space, but you can map the regions that represent the same face between higher and lower-dimensional spaces. Do it again, again, etc: take the limit as the resolution and dimensionality go to infinity. You can no more represent this explicitly than you can a real number, but you can use it as an abstraction, as a theory to tell you how well your approximations are working. --Josh ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303
