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The following bug has been logged on the website:

Bug reference:      18297
Logged by:          Alexander Lakhin
Email address:      exclusion@gmail.com
PostgreSQL version: 16.1
Operating system:   Ubuntu 22.04
Description:        

The following query:
CREATE TABLE a ();
CREATE TABLE b () INHERITS (a);
CREATE TABLE c () INHERITS (b);
CREATE TABLE d () INHERITS (a,b,c);

ALTER TABLE a ADD COLUMN i int;
fails with:
NOTICE:  merging definition of column "i" for child "d"
ERROR:  tuple already updated by self

While with a simpler hierarchy:
CREATE TABLE a ();
CREATE TABLE b () INHERITS (a);
CREATE TABLE c () INHERITS (a,b);

the column added successfully:
ALTER TABLE a ADD COLUMN i int;
NOTICE:  merging definition of column "i" for child "c"
ALTER TABLE

In the failed case the error occurred when table d was processed the third
time. First (following chain a -> b -> c-> d) the table got the column i
added, second (a -> b -> d) it got merged column definition, third
(a -> d) an attempt to merge the column definition once more failed.

This error can be seen at least on REL_12_STABLE .. master.