Re: Relation Definition

"Dawn M. Wolthuis" wrote
> I'll try this another way (persistence is my middle name?). I use a
> precise definition of "relation" from mathematics. It is in the glossary
> mAsterdam collected that I sent out a few days ago. However, it seems
> that most folks here use some other definition(s) of the term. When I try
> to get precision with this other definition, I find as many different
> definitions as there are writers. These are often not just other ways of
> saying the same thing, but really different definitions of what a
> "relation" is. I would like to know which ones are typically used by
> practitioners and/or theorists. It would be great if there were some
> general agreement on the definition, but I'd settle for having to work
> with 2-3 if needed.
>
> Is this one from Date the best in the industry? Can anyone suggest a
> better one?
>
> Date, C. "An Introduction to Database Systems", Addison Wesley 2004, p.
> 146
>
> " A relation value (relation for short), r say, consists of a heading and
> a body[4], where:
>
> --The heading of r is a tuple heading as defined in Section 6.2. Relation
> r has the same attributes (and hence the same attribute names and types)
> and the same degree as that heading does.
>
> --The body of r is a set of tuples, all having that same heading; the
> cardinality of that set is said to be the cardinality of r. (In general,
> the cardinality of a set is the number of elements in the set.)"
>
> Note: definitions of "relation type" and "relation type name" follow this
> definition.
> This definition relies on the definition of "tuple" and "tuple heading".
> Since his definition of "tuple" is also not the definition of a
> mathematical tuple, we also need to understand that from the below
> definition:
>
> p. 141 "Given a collection of types Ti (i=1, 2, ..., n), not necessarily
> all distinct, a tuple value (tuple for short) on those types--t, say--is a
> set of ordered triples of the form <Ai,Ti,vi>, where Ai is an attribute
> name, Ti is a type name, and vi is a value of type Ti, and:
> --The value n is the degree or arity of t
> --The ordered triple <Ai,Ti,vi> is a component of t.
> --The ordered pair <Ai,Ti> is an attribute of t, and it is uniquely
> identified by the attribute name Ai (attribute names Ai and Aj are the
> same only if i=j). The value vi is the attribute value for attribute Ai
> of t [1] The type Ti is the corresponding attribute type.
> --The complete set of attributes is the heading of t.
> --The tuple type of t is determined by the heading of t, and the heading
> and that tuple type both have the same attributes (and hence the same
> attribute names and types) and the same degree as t does."
>
> I'm thinking that def must be done at this point, and "tuple type name" is
> defined immediately following this quotation.
> This definition (of tuple) depends at least on the definition of "type"
> and it wasn't so easy to zero in on a definition from the text, so I'll
> quote what I think is the best I can find in this book:
>
> p. 111 "The data type concept (type for short) is fundamental; every
> value, every variable, every parameter, every read-only operator, and in
> particular every relational attribute is of some type. So what is a type?
> Among other things, it is a set of values.
> ...
> "We are trying to be reasonably precise in this part of the book.
> Therefore, instead of saying that, for example, type INTEGER is the set of
> all integers, we ought really to say that it is the set of all integers
> that are capable of representation in the computer system under
> consideration...
>
> Any given type is either system-defined (i.e., built in) or user-defined.
> ... Any type whatsoever, regardless of whether it is system- or
> user-defined, can be used as the basis for declaring relational
> attributes..."
>
> Since I haven't found where the rest of any such definition is in this
> book, I think perhaps we can just use the definition that a type is a set
> of values. The rest of this is descriptive and we would not want the term
> "relational" in the definition so we avoid a circular definitions.
>
> You can perhaps see why I work with the definition of a mathematical
> relation & mathematical tuples instead, but I really would like to know
> what database folks mean by these terms. If I want a very precise
> definition of relation as database relational theorists use the term, is
> this the best that the discipline has to offer?
>
> Thanks in advance. --dawn

This is not directed at you Dawn - but whatever happened to the KISS principle. Personally I usually suspect elaborate definitions (for a concept that would appear to me to be simple) as coming from high church adherents. My two bob's worth. Frank Received on Thu Feb 17 2005 - 12:56:52 CET