Abstract
We’ve seen several illustrations in previous chapters of the idea that certain dependencies imply others. To be specific, we saw in Chapter 7 how some FDs are implied by other FDs, and we saw in Chapters 9 and 10 how some JDs are implied by FDs. It’s time to take a closer look at such matters. Note that if we need to tell what normal form some given relvar is in, we do need to know all of the dependencies, implicit ones as well as explicit ones, that hold in that relvar. In this chapter, therefore, I plan to discuss among other things:
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Notes
- 1.
If we can assume the components X1, ..., Xn are all distinct, then we can drop part (b) of this definition.
- 2.
Of course, both JDs do hold in our running example, but that’s not because the ternary one implies the binary one (it doesn’t); rather, it’s because the FD {CITY} → {STATUS} also holds.
- 3.
As we know, other kinds of dependencies do exist, but I’m deliberately excluding them from consideration at this time.
- 4.
I note in passing that a proof of part (b) follows immediately from what Exercise 11.3, q.v., refers to as the converse of an extended version of Heath’s theorem.
- 5.
See David Maier, Alberto O. Mendelzon, and Yehoshua Sagiv: “Testing Implications of Data Dependencies,” ACM Transactions on Database Systems 4, No. 4 (December 1979).
- 6.
By the same token, don’t confuse equality generating dependencies and equality dependencies, which were described in Chapter 3.
- 7.
Strictly speaking, the premise tuples aren’t really tuples at all, because they contain variables instead of values. Likewise, the premise tuples taken together don’t really constitute a relation, either. I propose to overlook these points from here on, but I should at least mention that—partly for such reasons—the research literature typically refers to the initial set of premise “tuples,” and all other such sets appearing subsequently during the chase process, as constituting not relations but tableaux.
- 8.
See for example the book Foundations of Databases, by Serge Abiteboul, Richard Hull, and Victor Vianu (Addison-Wesley, 1995).
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© 2019 C. J. Date
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Date, C.J. (2019). Implicit Dependencies. In: Database Design and Relational Theory. Apress, Berkeley, CA. https://doi.org/10.1007/978-1-4842-5540-7_11
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DOI: https://doi.org/10.1007/978-1-4842-5540-7_11
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