Re: Relational lattice completeness


vc wrote:
Jan Hidders wrote:
vc wrote:
Jan Hidders wrote:
vc wrote:

What's confusing, to me at least, is that in another thread you said
that the question was about complete theories, that is about
completeness in the context of the first incompleteness theorem.

It is. Because we talking about a system where we have a semantical
notion of truth for algebraic identities and a syntactical one
(derivation from the set of given algebraic identies by applying them
to each other) and the question is if these two are the same.

They would be the same for a complete (in the sense of the first
incompletenes theorem) system so finding out whether this is the case
would amount to showing if the system in question is complete or not.

Not necessarily because the syntactical notion of truth is not the
usual one. It's related but not the same.

I let it slip the first time because I thought you'd used the
expression metaphorically, but now I am curious as to what exactly you
meant. The 1st incompleteness theorem talks about provability, not
truth. The notion of truth is not used in either the formulation or
proof.

It also doesn't mention completeness, so I thought you meant the notion
of completeness that it is usually assumed to say something about. But
this is all detracting form the main point. I gave an exact and, I
think, very simple definition in:

http://groups.google.be/group/comp.databases.theory/msg/a1c140fbe76681e8?hl=en&;

What did you not understand about it?

Let's assume that by 'syntactical notion of truth; you've meant in fact
derivation. If so, what did you mean by " because the syntactical
notion of truth is not the usual one. It's related but not the same" ?

We have different derivation rules.


Having a full and simple axiomatization makes it possible to write
query optimizers that do a more thorough search of the "optimization
space", and if you know you are complete then you are sure that you
need not look further for any other rules.

If you have a bunch of axioms/derivation rules, you can transform an
expression to your heart content regardless of whether the theory is
complete or not.

But you are not sure that you can find all possible query evaluation
plans, so you migh miss an optimization opportunity.

-- Jan Hidders

.

Relevant Pages

  • Re: Is basic research important?
    ... James Harris wrote: ... > but care more about the appearance of activity. ... > actions that they don't give a damn about truth or beauty. ... > A 12 year old can read my derivation and understand this post. ...
    (sci.physics)
  • please review: fully classical derivation of Plancks law
    ... The first, completely _classical_ derivation of Planck's law, replete ... Boltzmann constant k - to be precise, it serves the same role for the ... thermodynamic analysis of confined waves proving the completeness of ... standing wave modes ". ...
    (sci.physics.research)
  • Re: Mr Dawkins new book?
    ... "true/false" is one of possible qualities of predicates of some ... perfection (full completeness and consistency). ... completeness is not the earth shaking tragedy undermining Truth as some ...
    (uk.religion.christian)
  • Re: Relational lattice completeness
    ... Jan Hidders wrote: ... completeness in the context of the first incompleteness theorem. ... Not necessarily because the syntactical notion of truth is not the ...
    (comp.databases.theory)
  • Re: Sorry Godel - All Truths are Provable
    ... The set of true sentences of ... or somesuch. ... Neither negation completeness nor completeness of a logic have anything in particular to do with truth. ... The first is a purely syntactic property of a theory and the second is defined in terms of validity, not truth. ...
    (sci.logic)