Re: Codd's Information Principle

On Nov 6, 10:54 am, Cimode <cim..._at_hotmail.com> wrote:

I'm not sure if I can help you if my last post didn't.

> I thank you for your response and the effort you have put into

Appreciate that.

> > > The concept that a relational *operation* (projection) involving a
> > > relation R1 would also serve as a quantifier for the same relation is
> > > a concept I am having difficulties with.

I don't understand this sentence.
There aren't any quantifiers in the relational algebra. The quantifiers are in the corresponding predicate expression. (If you use relational domain or tuple calculus then the calculus expression looks just like the predicate expression.) That's why I wrote the quote that follows.

> > Use of a relation operation in a relation expression corresponds
> > to use of a connective or quantifier in the corresponding predicate
> > expression.
>
> That is precisely the concept I feel unconfortable with.

Well I'm sorry, but that's the whole point of the relational algebra.

Following my referenced message, an example.
relation R{X} with predicate PR "blah blah...X..."
relation S{X, Y} iwth predicate PS "foo bah..X...Y..."

> > > I would be glad to hear how we establish a valid quantifier in
> > > relational algebra using only internal predicates.

I don't understand this.
Maybe you mean quantifier in the sense of SUM(relation, expression) or or COUNT(relation) (or that matter (relation WHERE expression)). These actually involve relational calculus (pace Date and Darwen).
(But special case EXISTS(relation, attribute) corresponds to PROJECT OUT in the relational algebra.) As explained in Tegiri's reply to your post this requires some extension to the predicate
(and hence domain and tuple) calculus.
To use this notation we don't need to extend the relational algebra because you can define the meaning of such quantifier expressions in terms of iterated standard expressions.
No one is saying the relational algebra can handle this. But no one is saying you
have to limit yourself to the relational algebra, either. It's just some math that can do some stuff. Like predicate calculus or series notations.

> Only if you accept as a premice that an operation can also serve as a
> valid quantifier. There are other functions or intervals quantifiers
> that can increase the expressive power of algebra but they do require
> digging into domain analysis and combinatory analysis.

I don't understand this.
Maybe you mean generic quantifiers as addressed above.

> In
> traditional algebra, valid quantifiers are values not operations I
> do not see why ra should have the privilege to define its own rules on
> that perspective.

I don't understand.
We can define an algebra, ie a collection of values and operators on them, to act any way we want. Anyway, the quantifiers are not in the relational algebra, they are in the corresponding predicate expression.

> > > The lack of
> > > clarification of the external predicate, while being symptomatic
> > > limitation of traditional RM relational theorists gladly recognize,
> > > does not bother them much when it comes to operate relations
> > > algebrically using only the internal predicate.

I don't understand this.

> domain constraint analysis has been left out of
> relational algebric definition since it was prior to relational model
> definition.

I don't know what domain constraint analysis is, please give a reference.
I suppose you mean domain in the sense of problem domain, ie the world modelled by the database.
The relational model has nothing to say
about how you establish your predicates. It's just a way to automatically with a certain complexity calculate the tuples satisfying a predicate expression given the tuples satisfying some given predicates. No one's saying that's all the functionality we'd ever want.

> I do not see for instance how can such premice allow to develop a
> computing model for effectively representing data independence in the
> context of relation manipulation and operation.

I don't understand this.
Having data independence means that changing the structure but not meaning of data should be easy. If you express yourself structurally relationally then new (relational) structure can be described simply by relational expressions.

> I tend to think from current and past research that such premice leads
> to confusion and limits the expressive ability and opportunity to
> logically represent relational operations as a part of a turing
> complete machine.

The relational algebra was specifically designed so that 1. you could use predicate calculus as a (non-imperative) programming language and 2. it has a certain reasonable evaluation complexity. Ie it was designed to have limited expressive ability. (That's why there are no exact equivalents to NOT and OR in a relational dbms.)
No one is saying it should do any more.
(To use relational algebra as a non-evaluated notation, or if your system checks that your queries are "safe", you can introduce those equivalents.)

If you allow recursion then you leave this complexity. But people seem to be happy to still consider the dbms relational. If you allow a certain higher evaluation complexity (resolution) and a certain restricted notation (Horn clauses) you get logic programming.
For higher complexity yet you get constraint programming. Nevertheless relational algebra is still useful for giving non-imperative semantics for these other systems.

So I guess a lot of your intuitions are right, but I'd say you don't understand the basic properties and limitations of the relational model. (Also, I don't understand most of your post in detail.)

philip Received on Sat Nov 07 2009 - 02:19:07 CET