structurally when it is enforced using one of the constraints available in the relational model e.g. primary key, foreign key, check constraint, uniqueness constraints etc.
procedurally when it is enforced using some means outside the relational model e.g. a stored procedure, a trigger or some other kind of coding.
Procedural RI implies that something (a proc) needs to be called explicitly to enforce the RI. Structural implies that the RI is built into the database and so cannot be sidestepped ie FKs. If the above is true then surely triggers are structural and not procedural as mention above. Also at my current place we use Sybase with a database design tool to declare the FKs - this turns these FKs into triggers - what side of the fence would these FKs sit on?
Although it acts like DRI in the way describe I would put triggers as procedural. In effect the are like event prodecures in other languages - they are procedures that are triggered by events. How closely coupled they are with the database tables is not really the defining characteristic IMO.
That is an interesting point. Some databases (like ProstgreSQL) use triggers to enforce the foreign keys. However, in a situation like this, I believe the trigger usually calls a procedure. I know in PostgreSQL that triggers call trigger procedures. So in effect, although it is triggered automatically, it does call a procedure (depending on the situation).
But importantly, your statement that Procedural RI implies that something (a proc) needs to be called explicitly to enforce the RI has helped a lot. That really makes sense to me. And in the context of my example, it does make sense.
Out of the two FDs, you could definitely say that the FD Coordinator -> Faculty can be enforced structurally (with my new understanding of that term).
As for the other FD (Degree, Faculty -> Coordinator), it would be implementation-specific, and therefore, not clear-cut. Perhaps procedurally, perhaps structurally.
Thanks for helping me think through these concepts/definitions. It's been a great help.