Relation --Need for Radical Redefinition PDF

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Relation.....too fundamental to be ill-defined but is it well defined? Is it useful? Not quite according to me. I have my questions and reasons to redefine relation radically. Here is the proposal.
See the PPT by the same name on www.slideshare.net/putchavn
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Relation --Need for Radical Redefinition PDF

  1. 1. Putcha V. Narasimham Knowledge Enabler Systems Founder Professor & Proprietor Temporary Address: 1924, Hamilton Avenue, Belmon CA kenablersys@yahoo.com or putchavn@yahoo.com Relation---Need for Radical Redefinition Page No 1 of 6 The Best Anywhere Must Reach the Needy Everywhere Relation:NeedforRadicalRedefinition Our Ref: Footer Date: 25JUL13 I'm not smarter than anyone else, I just think about things more Albert Einstein Being competent, effective and efficient is 90% mindset and 10% toolset. ---Roger Tregear Putcha V. Narasimham Let’s start with A relation is any subset of a Cartesian product. For instance, a subset of A x B called a "binary relation from A to B is a collection of ordered pairs (a,b) with first components from A and second components from B. http://mathworld.wolfram.com/Relation.html 1. OBSERVATION When I applied this definition of "Relation" (to Entity Relationship Diagram and Associations in Object Oriented Analysis and Design), I found that there is “No Principle or Criterion" based on which ordered pairs may be
  2. 2. Putcha V. Narasimham Knowledge Enabler Systems Founder Professor & Proprietor Temporary Address: 1924, Hamilton Avenue, Belmon CA kenablersys@yahoo.com or putchavn@yahoo.com Relation---Need for Radical Redefinition Page No 2 of 6 The Best Anywhere Must Reach the Needy Everywhere Relation:NeedforRadicalRedefinition formed to represent WHAT are RELATED & HOW. There is no significance for the name of relation nor its meaning. 2. THE PROBLEM There seems to be a serious flaw. The definition simply enumerates the ordered pairs from two sets and calls it a relation. It lists which members of the two sets are related but fails to state what brings them into a relation and what the relation is. There is NO indication of WHY or HOW a relation may arise and how many kinds of relations may exist. This causes a problem in ascertaining if a "relation" is properly applied. This way, we only know who or which are related but NOT know what the relation is. A serious problem. 3. EXAMPLE Let's consider A, a set of men and B, a set of women and see the problems. 3A: If a relation "is husband of" is to be defined from A to B, one has to state the principle based on which a member of B is to be selected for a member of A. 3B: Similarly if a relation "is brother of" is to be defined from A to B, one has to state another principle based on which a
  3. 3. Putcha V. Narasimham Knowledge Enabler Systems Founder Professor & Proprietor Temporary Address: 1924, Hamilton Avenue, Belmon CA kenablersys@yahoo.com or putchavn@yahoo.com Relation---Need for Radical Redefinition Page No 3 of 6 The Best Anywhere Must Reach the Needy Everywhere Relation:NeedforRadicalRedefinition member of B is to be selected for a member of A. 4. NO BAISIS Not stating the criterion (or principle) of associating removes the basis of forming a set of ordered pairs. 4A: Consequently, what the “relation is” is not known till some sub-set of Cartesian Product between two sets is created but why or how any such subset may be formed is not known and so no valid subset can be formed. 4B: Some random subsets may be formed and any random subset would be a “relation” without any known properties since their formation itself is baseless or random. Of course, one may consider randomness itself to be a property and that may serve some purpose. Let it be. 5: HIDDEN CRITERIA It appears that some unstated but useful criteria are indeed applied in practice to form and verify relations, correcting the serious flaw in the definition but leaving the definition as such. 5A: In the example given in point 3, there is no basis to form or verify the relation “Is husband of” or “Is brother of” according
  4. 4. Putcha V. Narasimham Knowledge Enabler Systems Founder Professor & Proprietor Temporary Address: 1924, Hamilton Avenue, Belmon CA kenablersys@yahoo.com or putchavn@yahoo.com Relation---Need for Radical Redefinition Page No 4 of 6 The Best Anywhere Must Reach the Needy Everywhere Relation:NeedforRadicalRedefinition to the definition of relation but relation itself would be meaningless. 5B: Even when the ordered pairs are formed according to some criteria, there is no way to name the relation to refer to those criteria and carry the criteria as a part of relation. So, many factors are missing. 6: THE PRAPOSAL So, I find there is a need for Radical Redefinition of Relation for informed use / applications. Here is my proposal: 6A: Without knowing the principle of relation, no ordered pairs can be formed and called a relation. No relation can arise and abide (hold) between two sets whose members are arbitrarily paired even though ordered. A set of ordered pairs, not satisfying specified criteria of relation, is just a set of ordered pairs but NOT relation. 6B: From the sets A and B, if a new set of ordered pairs can be formed according to some criteria heretofore not known, the investigator cannot claim to have found a relation merely by enumerating the pairs. The investigator has to “necessarily fit a hypothesis to the observation and define the principle of
  5. 5. Putcha V. Narasimham Knowledge Enabler Systems Founder Professor & Proprietor Temporary Address: 1924, Hamilton Avenue, Belmon CA kenablersys@yahoo.com or putchavn@yahoo.com Relation---Need for Radical Redefinition Page No 5 of 6 The Best Anywhere Must Reach the Needy Everywhere Relation:NeedforRadicalRedefinition the relation and give a unique name to such relation”. 6C: Proposed definition: A relation between two sets A and B is a named set of principles and criteria, according to which ordered pairs can be formed from A and B This is a binary relation but it can be extended to reflexive and n-ary relations. All other properties and conditions of set theory hold. 6D: Some Properties of Relation:  Those who are related through any relation will be a subset of the Cartesian product of sets A and B.  The principles and criteria must be applicable to the sets involved.  For certain relations, ordered pairs may or may not exist.  The number of possible relations between any two sets may vary from Zero to many.  Two or more relations having the same ordered pairs are equivalent, if and only if the named set of principles and criteria to form them are also the same.
  6. 6. Putcha V. Narasimham Knowledge Enabler Systems Founder Professor & Proprietor Temporary Address: 1924, Hamilton Avenue, Belmon CA kenablersys@yahoo.com or putchavn@yahoo.com Relation---Need for Radical Redefinition Page No 6 of 6 The Best Anywhere Must Reach the Needy Everywhere Relation:NeedforRadicalRedefinition Pain of unresolved issues For long I lived in pain with what I found to be a flaw. I sought clarifications from many sources of knowledge---perhaps not the right ones. Unfortunately, none of them gave any convincing reasons for or against the original definition or the flaw pointed out or the proposed definition. That has been even more painful. I could be wrong It is possible that my thinking and understanding are flawed. I need to know what’s wrong and what the resolution is. LinkedIn and SlideShare provide excellent opportunities to discuss topics though all of them do not lead to agreement or resolution. Thinking & discussions help I have no claim to smartness. In fact, I have serious disappointment at not being smart enough. Yet, I believe thinking and discussion help. Comments with reasons and citation are most welcome. Thanks and regards, Cordially, Putcha V. Narasimham

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