Bitemporal sequenced unique constraint (function/trigger)

Hi there, This is my first time posting in here and I'm hoping somebody can point out where I am going wrong?

I am currently trying to use Bitemporal tables. By this I mean a table with a valid times and transaction times. These topics are covered by Joe Celko and Richard Snodgrass in their respective books.

I have developed a simple schema to test the relevant constraints which are required to keep all the valid times and transaction times in order and to make sure they don't overlap. This is shown below and is done using a similar schema of tables for Customers, Properties and Prop_Owners as Richard Snodgrass does in his book.

Of course these constrains are not possible in Postgres, so I have made them as functions and then created triggers for them.

Everything seems to be working except for my function/trigger that maintains the referential integrity between the Prop_Owner and Customers tables when there is a "gap" in the Customers valid time or transaction time.

I am using Postgres 8.1 on Suse10.2

vt = valid time
tt = transaction time

Here is the schema:

CREATE TABLE Customers
(customer_no INTEGER NOT NULL,
customer_name CHAR(30) NOT NULL,
vt_begin DATE DEFAULT CURRENT_DATE,
vt_end DATE DEFAULT DATE '9999-12-31',
tt_start DATE DEFAULT CURRENT_DATE,
tt_stop DATE DEFAULT DATE '9999-12-31',
CONSTRAINT Cust_VTdates_correct
CHECK (vt_begin <= vt_end),
CONSTRAINT Cust_ttdates_correct
CHECK (tt_start <= tt_stop),
PRIMARY KEY (customer_no, vt_begin, vt_end, tt_start, tt_stop)
);

CREATE TABLE Properties
(
prop_no INTEGER NOT NULL PRIMARY KEY,
prop_name CHAR(20) NOT NULL
);

CREATE TABLE Prop_Owner
(
prop_no INTEGER NOT NULL
REFERENCES Properties (prop_no),
customer_no INTEGER NOT NULL,
vt_begin DATE DEFAULT CURRENT_DATE,
vt_end DATE DEFAULT DATE '9999-12-31',
tt_start DATE DEFAULT CURRENT_DATE,
tt_stop DATE DEFAULT DATE '9999-12-31',
CONSTRAINT PropOwner_VTdates_correct
CHECK (vt_begin <= vt_end),
CONSTRAINT PropOwner_ttdates_correct
CHECK (tt_start <= tt_stop),
PRIMARY KEY (prop_no, customer_no, vt_begin, vt_end, tt_start, tt_stop)
);

Here is the function/trigger I seem to be having trouble with (although there are others which maintain the integrity of the data - meaning records cannot overlap):

CREATE OR REPLACE FUNCTION P_O_integrity() RETURNS TRIGGER AS
$$
DECLARE vald INTEGER;
BEGIN
SELECT 1 INTO vald
WHERE NOT EXISTS
(SELECT *
FROM Prop_Owner AS A
-- there was a row valid in <ReferencedTable> when A started
WHERE NOT EXISTS
(SELECT *
FROM Customers AS B
WHERE A.customer_no = B.customer_no
AND B.vt_begin <= A.vt_begin AND A.vt_begin < B.vt_end
AND B.tt_start <= A.tt_start AND A.tt_start < B.tt_stop)
-- there was a row valid in <ReferencedTable> when A ended
OR NOT EXISTS
(SELECT *
FROM Customers AS B
WHERE A.customer_no = B.customer_no
AND B.vt_begin < A.vt_end AND A.vt_end <= B.vt_end
AND B.tt_start < A.tt_stop AND A.tt_stop <= B.tt_stop)
-- there are no gaps in <ReferencedTable> during A's period of validity
OR EXISTS
(SELECT *
FROM Customers AS B
WHERE A.customer_no = B.customer_no
AND ((A.vt_begin < B.vt_end AND B.vt_end < A.vt_end)
OR (A.tt_start < B.tt_stop AND B.tt_stop < A.tt_stop))
AND NOT EXISTS
(SELECT *
FROM Customers AS B2
WHERE B2.customer_no = B.customer_no
AND ((B2.vt_begin <= B.vt_end AND B.vt_end < B2.vt_end)
OR (B2.tt_start <= B.tt_stop AND B.tt_stop < B2.tt_stop))))
);
IF NOT FOUND THEN
RAISE EXCEPTION 'Referential integrity breached. No covering Foreign Key';
END IF;
RETURN NULL;
END;
$$
LANGUAGE plpgsql;

CREATE TRIGGER P_O_integrity
AFTER INSERT OR UPDATE OR DELETE ON Prop_Owner
FOR EACH ROW EXECUTE PROCEDURE P_O_integrity();

It is this trigger/function (P_O_integrity) that does not work properly. Specifically it is the following part:

-- there are no gaps in <ReferencedTable> during A's period of validity
OR EXISTS
(SELECT *
FROM Customers AS B
WHERE A.customer_no = B.customer_no
AND ((A.vt_begin < B.vt_end AND B.vt_end < A.vt_end)
OR (A.tt_start < B.tt_stop AND B.tt_stop < A.tt_stop))
AND NOT EXISTS
(SELECT *
FROM Customers AS B2
WHERE B2.customer_no = B.customer_no
AND ((B2.vt_begin <= B.vt_end AND B.vt_end < B2.vt_end)
OR (B2.tt_start <= B.tt_stop AND B.tt_stop < B2.tt_stop))))

This can be rewritten as follows:

SELECT customer_no
FROM Prop_Owner AS A
WHERE EXISTS
(SELECT customer_no
FROM Customers AS B
WHERE A.customer_no = B.customer_no
AND ((A.vt_begin < B.vt_end AND B.vt_end < A.vt_end)
OR (A.tt_start < B.tt_stop AND B.tt_stop < A.tt_stop))
AND NOT EXISTS
(SELECT customer_no
FROM Customers AS B2
WHERE B2.customer_no = B.customer_no
AND ((B2.vt_begin <= B.vt_end AND B.vt_end < B2.vt_end)
OR (B2.tt_start <= B.tt_stop AND B.tt_stop < B2.tt_stop))));

And if run on the data below, should pull out customer_no's '2' and '3'.
But does not seem to select any of the rows in which there are gaps in Customers during the validity of Prop_Owner??

The data I used is as follows:
Customers:
customer_no |customer_name | vt_begin | vt_end | tt_start | tt_stop
-------------+--------------------------------+------------+------------+------------+------------
1 | keith | 2006-01-01 | 9999-12-31 | 2006-01-01 | 2006-12-31
1 | keith | 2006-01-01 | 2006-12-31 | 2006-12-31 | 9999-12-31
1 | keith | 2006-12-31 | 9999-12-31 | 2006-12-31 | 2007-12-31
1 | keith | 2006-12-31 | 2007-12-31 | 2007-12-31 | 9999-12-31
2 | simon | 2004-01-01 | 9999-12-31 | 2004-01-01 | 2004-12-01
2 | simon | 2004-01-01 | 2004-12-31 | 2004-12-01 | 9999-12-31 <=
2 | simon | 2004-12-31 | 9999-12-31 | 2004-12-15 | 9999-12-31 <=
3 | john | 2000-01-01 | 9999-12-31 | 2000-01-01 | 2001-01-01
3 | john | 2000-01-01 | 2001-01-01 | 2001-01-01 | 9999-12-31 <=
3 | john | 2002-01-01 | 9999-12-31 | 2002-01-01 | 9999-12-31 <=

The arrows indicate where there are gaps.

Properties:
prop_no | prop_name
---------+----------------------
1 | house
2 | flat
3 | penthouse

Prop_Owner:
prop_no | customer_no | vt_begin | vt_end | tt_start | tt_stop
---------+-------------+------------+------------+------------+------------
1 | 1 | 2006-02-01 | 9999-12-31 | 2006-02-01 | 2006-12-01
2 | 2 | 2004-02-01 | 9999-12-31 | 2004-01-01 | 2004-12-25
3 | 3 | 2000-02-01 | 9999-12-31 | 2003-01-01 | 9999-12-31

The 2nd and 3rd lines should have not been able to be inserted with the trigger as they "bridge" records with gaps in the Customers table.

I hope this makes sense and that someone can explain why the last part of P_O_integrity is not selecting the records covered with gaps correctly.

Thanks for any help you can give.
Keith