ontolog-forum
[Top] [All Lists]

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

 To: "'[ontolog-forum] '" "Mitch Harris" Wed, 11 Feb 2009 10:04:54 -0500
 - as you say, a tuple is a sequence of  things (a tuple is member of a product of sets), so, yes, ordered with possible repetition. The number of things in the tuple is n (the length of the sequence). So you can also call a tuple an n-tuple (the number explicitly specified). And then the adjective to describe it is n-ary (there are n places). The provenance: binary, ternary, quaternary,..., n-ary. double, triple, quadruple,...n-tuple.   - as to tuples fitting in to natural language, I'm not sure I see the trouble, just describe the position of each element in the relation. I'll leave it to others to elaborate if that is oversimplified.   --Mitchell A. Harris, PhDResearch Faculty (Instructor in Computer Science)Department of RadiologyMassachusetts General Hospital/Harvard Medical School -----Original Message-----From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of ravi sharmaSent: Wednesday, February 11, 2009 8:46 AMTo: [ontolog-forum]Subject: Re: [ontolog-forum] n-ary vs binary Pat C, Others Appealing, but sometimes we have "A relationship (Tuples)" tuples meaning in my context a set of ordered things, are these n-arys? How would tuples fit in Natural Language Syntax?-- Thanks.Ravi(Dr. Ravi Sharma)313 204 1740 Mobile On Wed, Feb 11, 2009 at 7:47 AM, Patrick Cassidy wrote: I prefer the n-ary forms, because it allows one to say:                  {PatC gave Book23 to Mary1256 on Date20090214Z-5}    This happens to be congenial to my English-native-language way of reading, making comprehension faster than with a set of binary relations.    Appropriate axioms can create the necessary and sufficient relation of this assertion to each of the binary assertions, if they are needed for some inference engine.    But I also feel that people should be able to use any mode of _expression_ they want, and that there should be axioms that can translate among  the different modes.   PatC   Patrick Cassidy MICRA, Inc. 908-561-3416 cell: 908-565-4053 cassidy@xxxxxxxxx   From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat HayesSent: Wednesday, February 11, 2009 1:47 AMTo: maharri@xxxxxxxxx; [ontolog-forum] Subject: Re: [ontolog-forum] n-ary vs binary     On Feb 10, 2009, at 4:45 PM, Mitch Harris wrote: PH, JS, et al.: Semantically, 'give' has three participants.  One or two may be omitted in a grammatical English sentence if they are obvious from the context.  But they exist, whether or not the speaker or 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 wellknown   It 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   office Pensacola                            (850)202 4440   fax FL 32502                              (850)291 0667   mobile phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes        _________________________________________________________________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  ``` _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (01) ```
 Current Thread Re: [ontolog-forum] New Book: "Narrative Information", (continued) Re: [ontolog-forum] New Book: "Narrative Information", Rich Cooper Re: [ontolog-forum] New Book: "Narrative Information", Pat Hayes Re: [ontolog-forum] New Book: "Narrative Information", Gian Piero Zarri Re: [ontolog-forum] New Book: "Narrative Information", John F. Sowa Re: [ontolog-forum] New Book: "Narrative Information", Pat Hayes Re: [ontolog-forum] n-ary vs binary, Mitch Harris Re: [ontolog-forum] n-ary vs binary, Pat Hayes Re: [ontolog-forum] n-ary vs binary - inverting the n-ary to binary mapping, queries ?, Frank Olken Re: [ontolog-forum] n-ary vs binary, Patrick Cassidy Re: [ontolog-forum] n-ary vs binary, ravi sharma Re: [ontolog-forum] n-ary vs binary, Mitch Harris <= Re: [ontolog-forum] Relationship: n-ary vs binary, Azamat Re: [ontolog-forum] Relationship: n-ary vs binary, Ravi Sharma Re: [ontolog-forum] Relationship: n-ary vs binary, Azamat Re: [ontolog-forum] Relationship: n-ary vs binary, paola . dimaio Re: [ontolog-forum] Relationship: n-ary vs binary, Azamat Re: [ontolog-forum] Relationship: n-ary vs binary, Pat Hayes Re: [ontolog-forum] Relationship: n-ary vs binary, Azamat Re: [ontolog-forum] Relationship: n-ary vs binary, Pat Hayes Re: [ontolog-forum] Relationship: n-ary vs binary, Azamat Re: [ontolog-forum] Relationship: n-ary vs binary, Pat Hayes