only trigger b2_ab will fire, even though it will update column beta.
Column beta eventually changed but you never issued an UPDATE command with beta in the SET clause. The trigger only care about the later.
And in fact triggers on a table should never re-issue an actual command against the same table or you end up with infinite triggers.
If i change the declaration of b3_bc by removing the column list or including column alpha,
things work as I expected and b2_ab cascades to b3_bc.
But that isn't how this works. There is no cascading. As soon as the UPDATE query is planned the set of triggers it is going to trigger is basically known and nothing those triggers do individually will change that (aside from raising an error). All you did by changing b3_bc is get it included in the ordered list of triggers that will be executed each time, and only when, an UPDATE command is executed against the named table.
If you still believe a meaningful change can be had here a concrete suggestion would be helpful. Otherwise maybe someone takes an interest at some point - but this particular confusion seems extremely rare.
