What the Heck is a Relation? From Tables to Cartesian Products to Logic

http://merrigrove.blogspot.com/2013/12/what-heck-is-relation-from-tables-to.html?m=1

by ludsan • 13 years ago

50 10 13 years ago

merrigrove.blogspot.com

chris_wot2• 13 years ago

You have the following material implications:

    EMPLOYEE(Daniel Smith, Marketing)  →  TRUE
    EMPLOYEE(Jebediah Vargas, Marketing)  →  FALSE

However, if the employee name in the function is not Daniel Smith but the employee is in marketing, the first predicate is true. How does that fit into relational databases?

P.S. Great article!

siddboots• 13 years ago

The arrow notation here is not material implication, but function evaluation. The function itself can be interpreted as an Indicator Function[1] for the employee set, or alternatively, as simply evaluating the predicate.

In terms of tables, the rows are exactly the subset of predicates that are TRUE. So FALSE statements like the second one are indicated by their absence in the employee table.

[1] http://en.wikipedia.org/wiki/Indicator_function

chris_wot2• 13 years ago

Thanks! I had no idea

tunesmith• 13 years ago

The followup article (http://merrigrove.blogspot.com/2013/12/the-occultation-of-re...) is really good, too. I particularly liked the concrete example of the "projection".

csense• 13 years ago

In mathematics, a relation is a set of ordered pairs.

Strictly speaking, the relations of database theory are different objects, but closely related. (Yes, I just made an awesome pun.)

I'm surprised that the author didn't include "a relation is a set of tuples" as a definition in the article. Also, absolutely nothing is said about viewing a relation as a graph.

cousin_it2• 13 years ago

I suspect that using unordered sets as the foundation for databases might have been a mistake, and ordered lists with allowed repetition would've made a better model, if only because they can model tables and query results equally well (ORDER BY, SELECT without DISTINCT). Is there a good reason why this road was not taken?

eru• 13 years ago

Would you want bag semantics for things like union and intersection then?

cousin_it2• 13 years ago

Yes, that sounds reasonable. I don't know very much about the practical uses of union and intersection in SQL, though.

AlisdairO• 13 years ago

In most actual implementations of relational DBs there's nothing to disallow repetition in a table - you just don't specify a primary key (or preferably have a unique primary key that's just an ignored surrogate).

The difficulty with caring about ordering in the relational model is that suddenly you're imposing a lot more constraints: when you're joining two tables, whose order 'wins'? If you say (for example) that left side wins, you then need to keep track of that order through your query.

k0n2ad• 13 years ago

"The self is a relation that relates itself to itself or is the relation's relating itself to itself in the relation; the self is not the relation but is the relation's relating itself to itself." - Kierkgaard

Sorry, had to chime in with that

What the Heck is a Relation? From Tables to Cartesian Products to Logic

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