Re: A Topological Relational Algebra in Lisp

On Sunday, January 11, 2015 at 5:25:31 AM UTC-8, Norbert_Paul wrote:

> I am interested in a discussion here, because it seemed that reviewers
> tended to frown on my (any my co-workers) work because, for example:

What database-oriented field(s) do you consider this work to be contributing to? (Eg the reviewers' and audiences'.)

Just because you are using relational operators and persisting doesn't mean you are involving "relational databases". Moreover just because you are using a relation(al) algebra doesn't mean you are being "relational" in the database sense.

Besides that, you are mostly using relation operators among others to implement non-relation operators on non-relation structures that are merely represented by relations among other structures. Moreover some of your relations are specifically limited to binary relations and some are specifically representing matrices. So really at best you could say you have a partly relation(al) algebra implementation of a topological space algebra, some of the parts and operators of which are actually relation-based in the relation(al) algebra sense.

But almost none of this involves relations in the "relational database" sense. You're just using relations as an appropriate abstract and implementation sturcture; you're not using them "relationally". Because the significance of the "relational" in "relational database" is that there is a certain correspondence between relation(al) algebra operators and logic non-terminals, in such a way that there is a certain correspondence between equivalent relation expressions and predicate expressions, in such a way that not only can one query (in the sense of logical deduction, not the trivial sense of evaluating a relation expression) using either notation but the result can be automatically evaluated with certain complexity and optimization opportunities.

Here is part of what I wrote a while ago here when someone asked about a similar situation where a paper discussed analogues of relational database theory and probablitiy distributions, after I read its abstract. You can just read "topological space" for "probability distribution".

On Wednesday, April 11, 2012 at 3:02:41 PM UTC-7, com..._at_hotmail.com wrote:
>
> A (named attribute) relation can be seen as a set of or mapping on multi(-named-)dimensional points. Functional dependencies are properties of relation values and expressions.
>
> Database relational operators are designed so that there is a correspondence between relation expressions and predicates (and predicate expressions aka wffs). The value of a relation expression is the extension of a corresponding predicate (and wff) where the relation value's attributes are the predicate's parameters (and the wff's free variables). A relation expression has an associated predicate (and wff) built from it in a certain way according to its operators and its variables' given predicates (and wffs). The fundamental theorem of the relational model is that IF the body of each relation variable's value is the set of tuples that make a given predicate (or wff) true THEN the body of each relation expression's value is the set of tuples that make that expression's predicate (or wff) true. Eg if the predicate of relation R is R(X,Y) "person X loves person Y" and the predicate of relation variable S is S(Y,Z) "person Y loves food Z" then the expression for (R JOIN S) PROJECT_AWAY Z is EXISTS Z [S(X,Y) AND R(Y,Z)] "there exists a Z such that person X loves person Y and person Y loves food Z" ie "person X loves person Y who loves some food".
>
> Probability operators for treating relations as probability distributions will do different things (in general) than database operators. They will satisfy different theorems.
>
> A relation with a functional dependency can represent a function. Composition and images are relevant in databases when a relation expression corresponds to a function's (or wff term's) value. To the extent that distributions are used as (relational or functional) mappings such representation-independent mapping-oriented operators will appear in that system.
>
> So what we can expect is that what the two systems have in common is... they both somehow involve a relation as a set of or mapping on multi(-named-)dimensional points. Correspondences between operators other than ones that are oriented to mappings would be coincidental. I don't call that much of an analogy/parallel.

It turned out like I predicted. (Although the paper's relation-based representation of probability distributions was simpler than I expected.)

So from reading your page http://pavel.gik.kit.edu/doc/howto.html (particularly sections Topological Data Model and Example Session) my not very topologically informed impression is that your work uses relation operators but isn't "relational" in the database sense. (Even when you select from relations, it's by wffs and oblivious to the relation(al) algebra making that both possible and unnecessary.) Of course, I could be missing "relational" analogues. I hope you will try to justify any you have found or will find in light of this message.

Perhaps I can distill it down to your system's notion of "query" merely being an expression of mostly non-relation operators calculating mostly non-relation results that are also somewhat implemented by relation operators, rather than an enquiry, even most of the time they involve relations. Received on Fri Jan 16 2015 - 10:05:34 CET