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

 To: "[ontolog-forum]" paola.dimaio@xxxxxxxxx Thu, 12 Feb 2009 21:03:37 +0700
 AzamatI remember reading with great interest that part of your bookwhich really opened up my mind to understanding relationshipswhat was it? chapter X? I hope it resonates sooner rather than later PDMOn Thu, Feb 12, 2009 at 8:54 PM, Azamat wrote: On Thursday, February 12, 2009 3:56 AM, Ravi wrote:   But for practical applications we need to know how to test whether a given relation (say a few triples described by same relation type) are conforming to Cartesian product of a set?   As a product of three sets, X, Y, and Z, a general Cartesian product is reduced to an ordered triple of class variables: X x Y x Z . The _expression_ on a Cartesian grid  is defined as the construct consisting of all ordered triples , where the members are the elements, individual variables, of the respective sets. Your experimental results or observations of some tripley related things could be depicted on 3D graphs or charts, on which, for instance, weeks (Time, X) will be connected with Dow-Jones (Index Number, Y) and interest rates (Economic fundamentals, Z); or commodity production figures with prices and calendar years, etc. Since the relations can be of many sorts, causal, temporal, spatial, quantitative, qualitative, formal, logical, to establish a specific type one looks at the nature of relatives, or components, origin and direction of dependency, correlation (statistics), as well as their formal properties.    RS: Are sets the same as subject and object pair, tied by the relation? If i got the question right, yes and no. As such, everything is connected with anything. For the sake of analysis, it is commonly identified two types of relationships: simple, pure or homogeneous, and complex, heterogeneous. The first type is composed of the same kinds of things as the relatives: 1. substances related with substances, individuals with individuals, objects with objects, as space relations; 2. states with states; qualities (quantities) with qualities (quantities); 3. changes with changes, processes with processes, actions with actions, events with events, as causality and time relations; 4. relationships  with relationships, as analogy and proportion.   The second type deals with different levels of relatives: 1. whole/part, with many different sorts; 2. universal/particular, as generalization or instantiation; 3. class/member, as membership or subsumption   Kant viewed relation as one of the canonic classes of things, ranking it as: i. the substance-property relation (subject-predicate) logic; ii. causality-dependence; iii. reciprocal relation (community, reciprocality, a relation of mutual dependence, action, or influence).  Summing up: Relationship is an ultimate criterion of any reference ontology candidate; for RELATIONSHIP IS A MUST IN STANDARD ONTOLOGY.   Many thanks for the discerning reading. Azamat Abdoullaev http://www.eis.com.cy     ----- Original Message ----- From: Ravi Sharma Sent: Thursday, February 12, 2009 3:56 AM Subject: Re: [ontolog-forum] Relationship: n-ary vs binary Azamat Great clarity and definition of relation – I guess what you describe ought to also factor in predicate analysis. But for practical applications we need to know how to test whether a given relation (say a few triples described by same relation type) are conforming to Cartesian product of a set? Are sets the same as subject and object pair, tied by the relation? Thanks for starting the Wiki page as well.. Ravi (Dr. Ravi Sharma) 313 204 1740 Mobile   From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of AzamatSent: Wednesday, February 11, 2009 11:55 AMTo: [ontolog-forum] Subject: Re: [ontolog-forum] Relationship: n-ary vs binary   Relation is a canonic class of any ontology. It is characterized by substantial properties and formal attributes. Of the material properties, there are their reality, nature and type and direction of dependency. Of the second, there are transitivity, symmetry, reflexivity, and n-ary, or cardinality, terms, or tuples, of domains, elements, components, or arguments). The typical mathematical reading of relation is an extensive set of ordered elements (as ordered pairs, Kuratowski, Wiener, Skolem; well-ordering axiom). There are two formal definitions of relationship deserving attention, http://en.wikipedia.org/wiki/Relation_(mathematics): i. [A relation R over the sets X1, …, Xk is a subset of their Cartesian product, written R ⊆ X1 × … × Xk.]. ii. [A relation R over the sets X1, …, Xk is a (k+1)-tuple R = (X1, …, Xk, G(L)), where G(L) is a subset of the Cartesian product X1 × … × Xk. G(L) is called the graph of L.] So, one can say "an n-ary relation is an ordered class of n-tuples, or it is an ordered class of (n+1) tuple". Three things are of importance here: 1. the components of relations are of the same kind and sorts, objects, persons, qualities, quantities, times; 2. ordering of relations, their direction, a triadic 'giving', tetradic 'paying' or triadic 'betweenness'; 3. the key sense of relationship is represented by the graph, indicating its nature and kind: if it's causal relation, temporal relation, spatial relation, semantic relation, logical relation, etc. Think of the complex case of social networks, where social relationships described in terms of nodes (agents) and ties (relationships), of different sorts and kinds, like as emotional, friendly, economical, political, or commercial links and connections.  Any general ontology missing the class of relation as the fundamental category of reality is internally defective. For example, there is a comprehensive scheme of categories of reality proposed by Chisholm, who divided Entia into Contingent things (States (Events) and Individuals (Boundaries and Substances) and Necessary things (States and Nonstates (Attributes and Substances).  Since the class of relationship is deprecated, the scheme is missing the adhesive of all things, Relationship, as well as Time and Space.     Azamat Abdoullaev                     _________________________________________________________________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  -- Paola Di Maio ********************************* ``` _________________________________________________________________ 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", 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 Re: [ontolog-forum] Relationship: n-ary vs binary, Azamat Re: [ontolog-forum] n-ary vs binary, Matthew West Re: [ontolog-forum] n-ary vs binary, Patrick Cassidy Re: [ontolog-forum] n-ary vs binary, Rich Cooper