>> I've already done this several times. I still don't comprehend.
> 
> OK, you understand boolean "and" and boolean "or", right? This is called 
> "propositional logic":
> 
>   If it rains, the street is wet.
>   It is raining.
>   Therefore the street is wet.
> That's propositional logic.
> 
> Go the next step, and you get first order predicate logic:
>   All ravens are black.
>   My bird is a raven.
>   Therefore my bird is black.
> 
> The "all X are Y" is universal quantification.
> 
> If you have "some X is Y", that's existential quantification. Usually 
> it's part of an expression involving universal quantification, like
>   "for all integers X, there exists a integer Y such that
>      if X is prime then Y is prime and Y > X."
> That's just saying there's no biggest prime. No matter what
> number we pick, if it's prime, there's some other number that's
> also prime and larger. (It's not a proof, just a statement of
> a boolean value. Proving the boolean is true is a separate step.)
> 
> Note also that the result is *one* boolean value. It's either true for 
> all X, or it isn't.

Hmm, OK. That seems simple enough. I guess the problem is that all that 
relational calculus stuff is abstracted to the point where it's just 
moving symbols around and it's difficult to determine how this is 
related to reality.

> There are, of course, standard rules of deduction, like
>   "for all X, pred(X)"
> is the same as
>   "not for some X, not pred(X)"
> and so on.

But, notably, if X being true implies Y being true, then X being false 
does not necessarily imply Y being false.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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