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From: Chris Menzel <cmenzel@kbssun1.tamu.edu> To: fritz@rodin.wustl.edu Cc: cg@cs.umn.edu, interlingua@ISI.EDU, srkb@cs.umbc.edu, E.Hunt@cgsmtp.comdt.uscg.mil, bhacker@nara.gov, duschka@cs.stanford.edu, genesereth@cs.stanford.edu, jksharp@sandia.gov, msingh@bcr.cc.bellcore.com, msmith@vax2.cstp.umkc.edu, roger@ci.deere.com, scott@ontek.com, sharadg@atc.boeing.com, skperez@mcimail.com, tony@ontek.com, zeleny@math.ucla.edu In-reply-to: <9409091531.AA08687@rodin.wustl.edu> (fritz@rodin.wustl.edu) Subject: Re: INTERNATIONAL STANDARD FOR LOGIC: CSMF Message-id: <94Sep9.120526cdt.9765@kbssun1.tamu.edu> Date: Fri, 9 Sep 1994 12:05:24 -0500 Sender: owner-srkb@cs.umbc.edu Precedence: bulk

Fritz, Thank you very much for your thoughtful reply. You wrote: Chris Menzel said of Scott domains: FL:>> Actors" in Conceptual Graphs are >> procedural. Genesereth has stated often that KIF is declarative >> and not procedural. To provide declarative semantics for >> procedures requires correct treatment of recursive functions, >> functions of functions, and programs which loop infinitely and >> never halt; this requires "reflexive" algebraic structures of >> partial functions like the continuous lattices of Dana Scott, which >> leads to domain theory and necessary distinctions which are >> strongly higher-order. CM:>Once again, mere quantification over functions, functions of >functions, etc. does not necessarily mean you are using a higher-order >logic. These are all first-order objects in set theory. Scott >domains in particular are definable (and typically, are defined, even >in Scott's own papers) in first-order set theory. Scott structures include continuous lattices. The required lattice definition "For every subset X \subseteq B, the supremum \bigvee X exists" is second order and strongly so (Dickmann, in Barwise & Feferman, p. 324). Sorry, I was unclear; I should have said Scott domains were "definable_1" in set theory in the sense introduced in my previous post, i.e., the definitions (stated in the language of set theory) pick out the right notions in a standard model of set theory. They are of course not first-order definable in the stronger sense that guarantees nothing unintended falls under the definition; for that you need to ensure that the "for every subset X \subseteq B" quantifier, if written in a second-order language, does indeed range over all subsets of B, and that's just what true second-order semantics guarantees. My question, once again, had *not* to do with the undeniable value and importance of higher-order model theory, but with whether, *in the context of an Interlingua*, using a higher-order language with the stipulation that it be interpreted with full higher-order model theory buys you any more than using first-order set theory with the stipulation that it be interpreted in a standard model. Best wishes, Chris Menzel ================================================================= Christopher Menzel | Internet -> cmenzel@tamu.edu Philosophy, Texas A&M University | Phone ----> (409) 845-8764 College Station, TX 77843-4237 | Fax ------> (409) 845-0458 =================================================================