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## Re: [ontolog-forum] n-ary vs binary

 To: maharri@xxxxxxxxx, "[ontolog-forum] " Pat Hayes Wed, 11 Feb 2009 00:46:38 -0600
 On Feb 10, 2009, at 4:45 PM, Mitch Harris wrote:PH, JS, et al.:Semantically, 'give' has three participants.  One or two may beomitted in a grammatical English sentence if they are obviousfrom the context.  But they exist, whether or not the speakeror listener knows who or what they are.To get back to a single relation that is stipulated rather than follow themany (interesting) lexical/semantic paths surrounding donation, let's stickwith 'give' having all three parameters.Which begs the question. But let us proceed. Let me make what I think is the appropriate summary (yes many of thefollowing are arguable, and have already been argued, but there it is):Given the ternary relation "Gives(A, B, C)"  (which happens to mean that Agave B to C) we can easily encode it as three binary relations: assign aunique x, then Gives1(x, A), Gives2(x, B), Gives3(x, C) is derivable fromthe ternary relation and one can reverse the derivation.Not quite. There is no 'assignment' and no requirement of uniqueness. The translation into case/role binary form simply refers to the existence of the giving action. Also, the translation is usually stipulated so that the original ternary (or whatever) relation becomes a predication establishing the event as having the appropriate verbal type, in this case a giving. So one gets the pattern:Foo(A, B, C)(exists (x)( Foo(x)  & FirsCaseName(x, A) & SecondCaseName(x, B) & ThirdCaseName(x, C) )where the appropriate case/role names depend on the particuiar verb, but often have 'agent' as the first one. Converting everything to binary has its benefits: homogeneousrepresentation, most concepts are already binary (except maybe databasetables).The most important advantages are (1) the case/role names identify the various arguments by name, making it easier to remember them (2) the second form allows partial information to be recorded and used naturally, and allows for arbitrary extensions, and (3) it also puts the actual event described by the verb phrase into the universe of discourse, allowing other properties and relations to be asserted about it. Finally (4) it  means that a relatively simple notation (such as RDF graph syntax, ie a labelled directed graph) can be used to represent what seem on the surface to be much more complicated facts. This is probably the origin of the idea that 'most' relations are binary, which is actually much less obvious. However, despite its simplicity, this equivalence/derivation is not wellknownIt is very well known in AI/KR, ontology engineering, formal logic and linguistics. Several widely used rule languages are based on it., and even when known it is counterintuitive to use (as humans usuallywrite these things).On the contrary, for rendering the meanings of simple English action sentences, it is actually in many ways more intuitive; and it supports important 'obvious' entailments. For example, if John gave a book to Mary, then it follows that Mary was given a book by John. Could the n-ary/binary debate be settled by allowing binary to be themachine language and n-ary be the higher level human written language?That is one way to proceed, but it ignores the intuitive and human-engineering advantages of the case/role form, such as its being easier to remember. This whole topic is a storm in a teacup. Real ontology engineering can all be done within binary languages such as RDF: this has been known for decades. For some purposes, allowing higher adicity relationships is advantageous, but even when they are possible, the classical case/role system is still widely useful. It is easy, if a little tiresome, to mentally translate back and forth between various surface conventions where needed, and also to write preprocessors which present any logical form in almost any way that a user feels comfortable with. Let everyone use their favorite notation, and we can easily translate between them when necessary. Pat H -- Mitchell A. HarrisResearch Faculty (Instructor in Computer Science)Department of RadiologyMassachusetts General Hospital/Harvard Medical School_________________________________________________________________Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxxShared Files: http://ontolog.cim3.net/file/Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1JTo Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx ------------------------------------------------------------IHMC                                     (850)434 8903 or (650)494 3973   40 South Alcaniz St.           (850)202 4416   officePensacola                            (850)202 4440   faxFL 32502                              (850)291 0667   mobilephayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes
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