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Reply-To: cg@cs.umn.edu Date: Thu, 11 Nov 93 08:19:17 CST From: fritz@rodin.wustl.edu (Fritz Lehmann) Message-id: <9311111419.AA10808@rodin.wustl.edu> To: uribe@cs.stanford.edu Subject: Higher-Order KIF and Conceptual Graphs Cc: boley@dfki.uni-kl.de, cg@cs.umn.edu, interlingua@isi.edu, phayes@cs.uiuc.edu

Dear Thomas Uribe, uribe@cs.stanford.edu You wrote, on my suggesting a higher-order semantics for KIF and Conceptual Graphs: >Um, Chapter 8 of the KIF reference manual describes how functions >and relations can be defined... Given these definitions, one can >proceed to quantify over them, and thus define functions of >functions, >relations over relations, and so on (i.e., the "individuals" over >which the functions and relations range over are functions and >relations themselves). As I said in my recent reply to Mike Genesereth: "Yes, one can _refer_ in KIF to countable sets, and sets of these sets, as reified objects. (This includes relations if interpreted as sets of finite, "ordered" sequences of objects.) It isn't clear to me how actual quantification on (the recursive closure of) these objects has adequately expressive semantics, though, if the interpretation is only First-Order." The problem is the quantification. So-called "Weakly Higher- Order" languages reify relations into individuals but do not have true higher-order quantification over them. "Strongly Higher-Order" languages have true higher-order quantification over ALL relations and this includes their recursive closure. A First-Order mock-up is not deemed to be quite the same thing. Concepts equivalent under one may be incomparable in the the other. A First-Order model- theoretic semantics for a weakly higher-order language is no higher- order semantics at all -- it is still just First-Order. My original email inquiry in September suggested strongly higher-order semantics, sacrificing formal completeness and compactness but gaining useful expressiveness. >> I think I've cited examples of about five or six. . . >Have these examples been sent out to the Interlingua list? >I don't recall seeing them... Yes they have. See my next email message. It turns out that the "about five or six" were closer to 50. Yours truly, Fritz Lehmann fritz@rodin.wustl.edu 4282 Sandburg, Irvine, CA 92715 USA 714-733-0566