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Re: A good book

From: Cimode <cimode_at_hotmail.com>
Date: 10 Jul 2006 10:28:18 -0700
Message-ID: <1152552498.142638.283220@h48g2000cwc.googlegroups.com>

Chris Smith wrote:
> Cimode <cimode_at_hotmail.com> wrote:
> > If you look for a math book about databases you won't find it...If you
> > look for a computing science book about mathematics you won't find:
> > they are interdependent but separate domains.
>
> Are you sure I won't find it? I can find rigorous mathematical
> treatments of most fields of computer science. For example, there are
> certainly rigorous treatments of compilers, automata and formal
> languages, decidability, type theory, algorithms (asymptotics and
> methods of termination proofs and the like, plus certain subfields such
> as graph algorithms that are developed in the context of deeper
> mathematical structures), programming language semantics, etc. etc. By
> "rigorous", I mean that the book actually proves its subject matter
> using an axiomatic method and a formal model, rather than merely
> speculating about things that it claims are true. I would assume that
> databases and the relational model fit in this category, as well.
You are dealing withe complex issue of relationship between mathematics and computing science.

The examples you pointed out are implementation issues. RM is not an implementation model but logical model. As a consequence, once could consider RM as a different language media for mathematic concepts. My point is that several mathematical concepts have been expressed in RM but not yet expressed in mathematics of relations. That's why several have considered RM an extension of relation mathematics as the relationship between the two fields is neither mutually exclusive nor unidirectional (at abstract level computing science is a science of its own). For instance, several mathematical theorem and demonstration (recursive) have been proven wrong and revised after computing science have been proving them false on high enoug numerical values.

> If such a thing really doesn't exist for the relational model of
> databases, that would be rather surprising and disappointing; this
> especially, given how frequently the idea is brought up that relational
> databases are on a solid mathematical footing and that provides all
> manner of advantages. If that's not the case, then I may have to lower
> my expectations a bit. Certainly there's no irreparable harm in their
> being lowered, as many areas of applied software engineering lack such a
> formal theory; but I really rather hope that you are incorrect, and that
> there are such treatments of the relational model for databases. That
> others seem to think so gives me hope.
As I said, relationship between math and computing science is not that obvious. But for RM, if you feel more secure (which I perfectly understand) going through mathematics theory, I suggest you read first the following from Kurt Godel

*On Formally Undecidable Propositions of Principia Mathematica and Related Systems*

Once done you will realize that RM (sound) readings are just another expression of the same principles.

> Incidentally, I'm going to stop responding in this thread until I manage
> to actually read some of the sources suggested thus far. I hope no one
> thinks I'm ignoring them.
>
> --
> Chris Smith - Lead Software Developer / Technical Trainer
> MindIQ Corporation
Received on Mon Jul 10 2006 - 12:28:18 CDT

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