Is A Data Model An Abstraction?

Rob brings up a good point in his comment on The Problem of Abstraction in Definitions of Data (http://definitionsinsemantics.blogspot.com/2011/12/problem-of-abstraction-in-definitions.html).  He notes that what I am describing is not really abstraction but really a number of different things.
Today it seems the term "abstraction" is used in all kinds of situations when talking about data.  For me, it is often difficult to figure out what "abstraction" is supposed to mean in any one of these situations.  I strongly suspect that at least sometimes it does not really mean anything.  Sometimes I suspect it is even used for marketing hype.

The entry for "abstraction" in Baldwin's Dictionary of Philosophy and Psychology describes how abstraction is filtering out of attributes from an instance or a concept to achieve a particular view of the instance or concept.  Rather poetically the entry describes how a child looks at a body of water and becomes fascinated by the lustre caused by the play of sunlight on the surface of the water, to the exclusion of all the other qualities (attibutes) of the water.

This traditional understanding of abstraction as creating a view by filtering out attributes can be used in a special way to create the generalization hierarchies of genus and species (a.k.a. supertype and subtype, or general concept and specific concept).  The particular attributes of a group of specific concepts are left behind and attributes that the concepts have in common remain.  These are used to form the general concepts that include the specific concepts. 

However, abstraction as filtering out of attibutes can generate other perspectives.  Abstraction does not always have to lead to the traditional generalization hierarchy.  I can understand a man's watch as a timepiece, or a piece of jewelery, or as a fashion accessory.

Now, Rob is right in that I was not using "abstraction" in the above senses.  However, I do not have a better term to use for what I was trying to describe.  The main idea I was trying to get across is that one concept system can describe or specify another - such as how a  data model describes a physical database.  The relationship of "description" here is different to every other kind of relationship because the concepts present in the concept system being described have to have some kind of presence in the concept system doing the the describing.  This is not the same class of relationship we see in e.g. "I own a car".

So we somehow have the presence of a concept being described (e.g. a column of a physical database table) in a concept system doing the describing (e.g. an attribute of an entity type in a data model).
Rob terms this "representation" (If I understand his comment correctly).  This has to be right.  However, a representation can often be a picture - a mere image.  Technically, this is called a "phantasm" because it does not have the attributes differentiated from the whole.  Unfortunately, the process of recognizing and separating the attributes from a phantasm is also called abstraction.  It gets more complicated.  we cannot take a photograph of a physical database and produce anything like a data model.  A database has to be conceieved, not imagined.

Obviously, we are getting into a whole lot of other issues here.  I cannot really defend myself against Rob's criticism of my having overloaded (or over-abstracted?) the term "abstraction".  However, I do not have a commonly accepted set of terms that I can use to convey the idea of one concept system describing another.  More of an excuse than a reason, but it will have to do for now.

The Problem of Abstraction in Definitions of Data Objects

I think there is a major problem in not being able to understand and work with different levels of abstraction.  By "abstraction" in this sense I mean one concept system that somehow describes or defines (not merely relates to) another concept system.  I think this is a big problem for definitions in data models.

Let us take an example in a retail business such as mortgage banking: Customer Name.  Customer Name exists in the business.  They use it all the time.  Maybe it is sometimes called Borrower Name, but the concept is the same.  This is the Level 1 abstraction.

Now let us think of data values in a column in a table that holds Customer Name.  These data values are stored as a code of 1's and 0's.  Of course these bits are rendered into something we can read.  However, this is not the same as the Customer Name in the business.  I worked for a place where they prefixed the name of anyone who had recently left with "ZZZ".  So we could have "ZZZ_John Smith" as a data value, but the business would call him "John Smith" still.  The data value is the Level 2 abstraction.

Now let us think of the column itself that stores Customer Name, irrespective of whatever it contains.  This is the container used for the data.  It is merely a container, and anything can be put into it - just in the same way as the old peanut jelly jar I have on my desk is used to hold pens.  The column has certain characteristics, like the maximum length of text it can hold.  This is the Level 3 abstraction.

Now let us think of the data model that describes the column that will hold Customer Name.  In this, Customer Name is an attribute.  We worry about what naming convention to give it.  And behold!  Our data modeling tool asks us to enter a definition for Customer Name!  Yet, we are now at Level 4 of abstraction.

Let's summarize.  The concept system of the data model (Level 4) is a design for the concept system of the container of the data (Level 3) which will store the concept system of data values (Level 2) which we hope will satisfy the concept system of the information needs of our users (Level 1).

So tell me again what the definition entered in the data model is referring to?  Which of the four concept systems?.  Suppose it is stated as "an attribute that holds customer name" - I have seen this kind of thing quite often.  Well, an attribute is something in a data model (Level 4), and a thing that holds data is a container (Level 3).  

It would seem that the ideal thing would be to understand the Level 1 abstraction - the business information.  However, the chances of getting a good definition of this when you are at Level 4 would seem to be a challenge.  There are too many layers of abstraction in the way.  This, I think, is why semantics are so important.  They deal with business information as is, and do not have to worry about other concept systems.

Dodd-Frank "Swap" - A Definitional Disaster?

The Dodd-Frank Act is intended to reform the financial system in order to reduce the chance of any future systemic failure.  Obviously, it is very important, and one of the most important parts of Dodd-Frank revolves around swaps.  It may be recalled that lack of understanding about Credit Default Swaps (CDS) was a big part of the financial crisis that began in 2008 - and specifically caused AIG to fail.  CDS, however, are only one species of swap.  Prior to 2008 there had been little regulation of swaps.

Before we go further, there is one other piece of background for those unfamiliar with the sausage-making process of US financial regulation.  An Act of Congress is just the beginning.  Agencies of the US government must take the Act and turn it in to rules - usually many rules - and then enforce them.  This means that if there is a problem in the Act, there can be difficulties across many rules.

Back to swaps.  The Dodd-Frank definition of "swap" is given below.  It is a pretty mind-numbing read.  This definition clearly shows that there is no simple definition of a swap.  The definition has a long list of concepts that are included, and a long list of concepts that are excluded (Paragraph B).

What we have is a collection of "things" that the government wants to be regulated in an identical manner - as "swaps".  However, the only consistency is the way these "things" are to be regulated.  There is no consistency - no common attributes intrinsic to these things - that distinguishes them from other things.  If there was a set of common characteristics, then these would presumably have been listed.  Instead, we get enumeration of members of the class (a practice frowned upon by traditional logicians). This is seen especially in the items labelled "(I)" through "(XXII)".  These are part of the definition, not a list of illustrations.

The definition even abstracts from enumeration of members when it says:  "(iv) that is an agreement, contract, or transaction that is, or in the future becomes, commonly known to the trade as a swap".  

I was shocked when I first read this.  How can a definition simply point back to common usage of a term?  The government is throwing the burden of definition back on the speech community!  Even then, what is meant by "the trade" and "commonly known" is puzzling (I cannot find definitions for these terms in the Act).  Also, if some bright investment banker figures out a new product that he or she brands as something other than a swap, then they can presumably escape regulation.  However, there is an "escape hatch" - the Commodities Futures Trading Commission (CFTC) is delegated the authority to broaden the definition, which should prevent this kind of problem.  But suppose something gets called a "swap" that is nothing like a "real swap".  That sort of thing happens all the time in the evolution of language.  There is no way the definition can be modified to exclude it as the Act is written. 

There is a lot more to be said on the Dodd-Frank definition of "swap" and we will cover more topics in future posts.  This post is merely an appetizer to what promises to be a true feast of lessons that can be drawn about definitions.

Here is the defintion of "swap" - only subparagraphs (A) and (B) of the text - subparagraphs (C) through (F) are not part of the general definition.  The full text of the Act can be found at: www.sec.gov/about/laws/wallstreetreform-cpa.pdf - please refer to Section 721 and scroll down until you see "SWAPS".

‘‘(47) SWAP.—
‘‘(A) IN GENERAL.—Except as provided in subparagraph (B), the term ‘swap’ means any agreement, contract, or transaction—
‘‘(i) that is a put, call, cap, floor, collar, or similar option of any kind that is for the purchase or sale, or based on the value, of 1 or more interest or other rates, currencies, commodities, securities, instruments of indebtedness, indices, quantitative measures, or other financial or economic interests or property of any kind;
‘‘(ii) that provides for any purchase, sale, payment, or delivery (other than a dividend on an equity security) that is dependent on the occurrence, nonoccurrence, or the extent of the occurrence of an event or contingency associated with a potential financial, economic, or commercial consequence;
‘‘(iii) that provides on an executory basis for the exchange, on a fixed or contingent basis, of 1 or more payments based on the value or level of 1 or more interest or other rates, currencies, commodities, securities, instruments of indebtedness, indices, quantitative measures, or other financial or economic interests or property of any kind, or any interest therein or based on the value thereof, and that transfers, as between the parties to the transaction, in whole or in part, the financial risk associated with a future change in any such value or level without also conveying a current or future direct or indirect ownership interest in an asset (including any enterprise or investment pool) or liability that incorporates the financial risk so transferred, including any agreement, contract, or transaction commonly known as—
‘‘(I) an interest rate swap;
‘‘(II) a rate floor;
‘‘(III) a rate cap;
‘‘(IV) a rate collar;
‘‘(V) a cross-currency rate swap;
‘‘(VI) a basis swap;
‘‘(VII) a currency swap;
‘‘(VIII) a foreign exchange swap;
‘‘(IX) a total return swap;
‘‘(X) an equity index swap;
‘‘(XI) an equity swap;
‘‘(XII) a debt index swap;
‘‘(XIII) a debt swap;
‘‘(XIV) a credit spread;
‘‘(XV) a credit default swap;
‘‘(XVI) a credit swap;
‘‘(XVII) a weather swap;
‘‘(XVIII) an energy swap;
‘‘(XIX) a metal swap;
‘‘(XX) an agricultural swap;
‘‘(XXI) an emissions swap; and
‘‘(XXII) a commodity swap;
‘‘(iv) that is an agreement, contract, or transaction that is, or in the future becomes, commonly known to the trade as a swap; ‘‘(v) including any security-based swap agreement which meets the definition of ‘swap agreement’ as defined in section 206A of the Gramm-Leach-Bliley Act (15 U.S.C. 78c note) of which a material term is based on the price, yield, value, or volatility of any security or any group or index of securities, or any interest therein; or
‘‘(vi) that is any combination or permutation of, or option on, any agreement, contract, or transaction described in any of clauses (i) through (v).

‘‘(B) EXCLUSIONS.—The term ‘swap’ does not include—
‘‘(i) any contract of sale of a commodity for future delivery (or option on such a contract), leverage contract authorized under section 19, security futures product, or agreement, contract, or transaction described in section 2(c)(2)(C)(i) or section 2(c)(2)(D)(i);
‘‘(ii) any sale of a nonfinancial commodity or security for deferred shipment or delivery, so long as the transaction is intended to be physically settled;
‘‘(iii) any put, call, straddle, option, or privilege on any security, certificate of deposit, or group or index of securities, including any interest therein or based
on the value thereof, that is subject to—
‘‘(I) the Securities Act of 1933 (15 U.S.C. 77a et seq.); and
‘‘(II) the Securities Exchange Act of 1934 (15 U.S.C. 78a et seq.);
‘‘(iv) any put, call, straddle, option, or privilege relating to a foreign currency entered into on a national securities exchange registered pursuant to section 6(a) of the Securities Exchange Act of 1934 (15 U.S.C. 78f(a));
‘‘(v) any agreement, contract, or transaction providing for the purchase or sale of 1 or more securities on a fixed basis that is subject to—
‘‘(I) the Securities Act of 1933 (15 U.S.C. 77a et seq.); and
‘‘(II) the Securities Exchange Act of 1934 (15 U.S.C. 78a et seq.);
‘‘(vi) any agreement, contract, or transaction providing for the purchase or sale of 1 or more securities on a contingent basis that is subject to the Securities
Act of 1933 (15 U.S.C. 77a et seq.) and the Securities Exchange Act of 1934 (15 U.S.C. 78a et seq.), unless the agreement, contract, or transaction predicates the purchase or sale on the occurrence of a bona fide contingency that might reasonably be expected to affect or be affected by the  creditworthiness of a party other than a party to the agreement, contract, or transaction;
‘‘(vii) any note, bond, or evidence of indebtedness that is a security, as defined in section 2(a)(1) of the Securities Act of 1933 (15 U.S.C. 77b(a)(1));
‘‘(viii) any agreement, contract, or transaction that is—
‘‘(I) based on a security; and
‘‘(II) entered into directly or through an underwriter (as defined in section 2(a)(11) of the Securities Act of 1933 (15 U.S.C. 77b(a)(11)) by the issuer
of such security for the purposes of raising capital, unless the agreement, contract, or transaction is entered into to manage a risk associated with capital raising;
‘‘(ix) any agreement, contract, or transaction a counterparty of which is a Federal Reserve bank, the Federal Government, or a Federal agency that is
expressly backed by the full faith and credit of the United States; and
‘‘(x) any security-based swap, other than a securitybased swap as described in subparagraph (D). 
...
(b) AUTHORITY TO DEFINE TERMS.—The Commodity Futures Trading Commission may adopt a rule to define—
(1) the term ‘‘commercial risk’’; and
(2) any other term included in an amendment to the Commodity Exchange Act (7 U.S.C. 1 et seq.) made by this subtitle.
(c) MODIFICATION OF DEFINITIONS.—To include transactions and entities that have been structured to evade this subtitle (or an amendment made by this subtitle), the Commodity Futures Trading Commission shall adopt a rule to further define the terms ‘‘swap’’, ‘‘swap dealer’’, ‘‘major swap participant’’, and ‘‘eligible contract participant’’.

A First Note on Partial Definitions

I think that partial definitions exist, and there are practical reasons for being interested in them.  I cannot find any literature about them, and this post is my first attempt at dealing with partial definitions.

The only conceptualization of a partial definition that I have figured out in any detail can be summarized by the formula:

Partial Definition = Name of Concept System + Type of Relation in Concept System

E.g., for "Wristwatch"

Definition of "Wristwatch" = "A type of timepiece"

Obviously, this parallels the Aristoteialan formula of Definiton = Genus + Specific Difference.  However, I think that Aristotle commits definitions to being only in a Concept System of generic relations (supertype-subtype to our data modeling friends).  Other types of Concept System exist, e.g. partative (part-whole), and associative. 

In a partial definition we provide information by locating the concept to be defined within a particular Concept System, giving context to the minds we are communicating with.  Of course, we must expect that these minds know about the Concept System we name in the partial definition.

The Concept System does not have to be a proximate Genus, as Aristotle would like.  It could be a much higher level generic concept, though this may broaden the context too much.  In the above example, locating "Wristwatch" in the concept system "Timepiece" provides more precise context than if I said "A type of instrument", "instrument being a more generic concept containing "Timepiece".  Obviously, there is skill required to choose the level appropriate to the mind being communicated with.

There is also the choice of Concept System to locate the concept in.  For "Wristwatch" I could have alternative partial definitions such as "A fashion accessory", or "An item of jewelery".  These identify different Concept Systems within which I wish to locate "Wristwatch" for whatever my purposes may be.

The Type of Relation in the Concept System in my formula above (e.g. "type", "part", "item") is one level of abstraction up from a description of the Concept System itself.  I think it serves to reinforce the essence of the Concept System.

While full definitons are not something we work on every day, I think partial definitions are very common in everyday communication. 

That's enough for now.  To summarize (and these points may need further proof): 

• Partial Definitions exist
• A common kind of Partial Definition is to locate a concept in a Concept System
• The Partial Defintion also describes the type of relation that predominates in the Concept System
• There is skill in selecting the Concept System as one concept can belong to many Concept Systems
• There is skill in selecting the level of generalization of the Concept System
• Partial Definitions are very common in everyday language (does that mean that everyone is an ontologist?)