Re: Relation subset operators
Date: Sun, 7 Jun 2009 04:46:57 -0700 (PDT)
> Now into the main topic -- set equality join.
I am not sure that is actually the main topic. In my perception, the specific problem which was adressed was the opportunity of using a new operator to simplify relation handling in the context of relational division. set equality is only but one aspect of operations that could potentially be expressed more effectively using such operator. I hoped that using questions would help clarify the scope but I am realizing I was wrong.
> I prefer to focus on set
> equality rather than set containment because I expect it to have nicer
> algebraic properties.
I am curious as to why you think that the idea of creating a new operator is *only* about *set containment*. As expressed the example provided (Question 1 to Question 8). The idea behind creating a new operator was actually that such operators allows a simpler but logically sound formulation of some operations that are tedious to express using traditional operators.
> For one thing, set equality join is commutative,
> and set containment is not. Because set join is essentially universal
> quantifier, and the later is often is written as "/\" (capital join
> "^"), lets choose the notation appropriately, so that set equality
> join of relations x and y is written as x/\y. What is set equality
> join algebraically in terms of our basic operations?
I would really appreciate if you could express the Questions proposed (and only the Questions proposed), using the relations proposed (and only the relations proposed), but using the notation you are more confortable with. It would help me greatly to relate to the arguments you are developping to apprehend the problem I am trying to address, but through your angle. It will also allow me adapt my communication to the logical tools you are using to verify correctness... Too many times, differences in notations make it difficult for people to exchange information into an effective way and tend to create dispersion as to solve well defined problems (call it another sign of immaturity of relational theory). That is why, I promote first the focus onto a single problem and make the effort of understanding somebody else notation. Received on Sun Jun 07 2009 - 13:46:57 CEST