# Re: Codd's Information Principle

Date: Fri, 6 Nov 2009 14:00:24 -0800 (PST)

Message-ID: <8095ed4c-f5cb-43d6-b089-62e29c443862_at_x6g2000prc.googlegroups.com>

On Nov 6, 10:54 am, Cimode <cim..._at_hotmail.com> wrote:

> ... In traditional algebra, valid quantifiers are values not operations. ...

I don't think there is universally agreed concept of quantifier for algebra. Carrying over quantifiers from logic, one may suggest that summation (http://en.wikipedia.org/wiki/Summation), product, infimum, and supremum are quantifiers (they are essentially generalizations of binary operations: addition, multiplication, meet, and join, correspondingly). It is common in algebra to represent qunatified operation in terms of binary ones; example:

1 + 2 + 3 + 4 + ... + n = n/(1-n)

Likewise, relational calculus quantified expression

R(x,1) <OR> R(x,2) <OR> R(x,3) <OR> ...

(assuming positive integers domain {1,2,3,...} for y). This repeated application of binary operation evaluates to binary operation: set intersection join:

D(y) set_intersect R(x,y)

where D(y) is domain of y (which we assumed earlier to be {1,2,3,...}). The last expression evaluates to projection which is well known fact, but misses the big idea that universal and existential quantifiers are dual quantifiers. Logical quantifiers in algebraic form are set joins (which in some cases evaluate to projection and relational division). Received on Fri Nov 06 2009 - 23:00:24 CET