How to represent "not exists" in relational algebra?

How do I rep开发者_Go百科resent the SQL "not exists" clause in relational algebra?

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The SQL NOT EXISTS construct can be represented in relational algebra by the antijoin ▹.

The antijoin L ▹ R of two relations L and R selects those tuples of L that do not join with any tuple in R. It can be defined in terms of set difference and left semijoin as follows:

L ▹ R = L - (L ⋉ R).

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I think you're looking for the existential quantifier (∃), which you could then negate (~∃).

Response to comment: I don't remember most of my relational algebra, but if I was going to take a stab at it I would guess something along the lines of: σ_∃σ(Y)(S). Or possibly π_∃π(Y)(S); I don't quite remember if you'd want selection or projection for that.

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In my case I solved this issue by rewriting the query,

SELECT *
FROM contactperson
WHERE EXISTS(
   SELECT *
   FROM person
   WHERE contactperson.personId = person.id)

to:

SELECT *
FROM contactperson
WHERE personId = (
   SELECT id
   FROM person
   WHERE contactperson.personId = person.id)

It returns the same result and is easier to rewrite to relational algebra using a join.