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Date: Fri, 22 Mar 96 20:50:43 CST From: fritz@rodin.wustl.edu (Fritz Lehmann) Message-id: <9603230250.AA22956@rodin.wustl.edu> To: cg@cs.umn.edu, ged@cs.rmit.edu.au, sowa@west.poly.edu Subject: Re: Availability of the ANSI standard proposal? Cc: goolsbey@cyc.com, interlingua@isi.edu, murray@cyc.com, srkb@cs.umbc.edu Sender: owner-srkb@cs.umbc.edu Precedence: bulk

Dear Conceptual Graphs, Interlingua and SRKB lists, John Sowa recently mentioned the hierarchy on relations. This is essential. There are a couple of subtleties to consider. First. decide what to do about converses of relations. If x R1 y subsumes x R2 y, and R2' is the converse of R2, then x R1 y subsumes y R2' x. An algebraic formalization is in Henkin, Monk & Tarski's "Cylindric Algebras". Keep in mind that, as Peirce noted, a triadic relation has five "converses" and it gets much worse with higher valence relations. Some time before I started working on Cyc, they decided to drop converses entirely. This was a very wise decision, I believe. If you think of a relation "floating" in abstract space, the converse(s) are really matters of how the abstract relation is projected into a string notation. There is only one genuine relation represented by all the converses. As I said on these lists years ago, West-Of(Kansas,Missouri) and East-Of(Missouri,Kansas) both represent the SAME FACT. Of course, to translate to other (string-based) languages and logics, it may be necessary to choose one variant or another, or all of them, depending on what the other language or logic requires. For inference and other purposes, Cyc needs only one form for each relation. If you want to switch the order then state it in a different order in CycL. I recommend that Conceptual Graphs people and others consider making the same choice, especially since the superfluity of converses is due to the (hyper)graph nature of logical relations. Had linear string notations for logics (and languages) never been devised, there would be little notion of "converse". The existence of converses is due to the linear form of natural languages. In the fundamental logic, i.e. abstract relational structures (directed hypergraphs floating in the Platonic void), the converses don't exist. This leads to an issue for relational subsumption though, and that is that there is an extra element of the subsumption of relations, namely the particular projection (permutation if you preserve valence) of the subsuming argument-positions into the subsumed argument-positions. If the relation is wholly symmetric then it doesn't matter. If the relation is partly symmetric (in only some argument-positions) then only the asymmetric arguments are of concern. For two arguments, allow for a swap, etc. Another thing to address is whether a relation can subsume another relation of different valence. I temporarily recommend against this. Consider also the case of "polyvalence" relations -- there is no good reason to require that a relation have fixed valence. KIF fortunately allows polyvalent relations (at least it used to in version 3.0). So does Cyc. In subsumption, handle these with care, but there should be no serious problem. (Note: My opinions on things like this are my own, not Cycorp's, especially since Cyc people are unaccustomed to treating logic as "floating hypergraphs". Other than that, my views are as authoritative, canonical and definitive as they ever were.) Yours truly, Fritz Lehmann Cycorp, 3500 W. Balcones Center Dr., Austin, Texas 78759 fritz@cyc.com