This algorithm has been named the naive algorithm for datalog evaluation. The basic idea of the semi naive algorithm is to concentrate, to the extent possible, on the new facts generated at each level and thereby avoid recomputing the same facts." — Foundations of Databases (TOC).

The difference between the naîve and semi-naîve evaluation in Datalog is that when you're evaluating using the naïve implementation you take all the initial dataset (existing EDBs) plus the news ones (inferred EDBs) for each iteration. For example, if you have the IDBs like this:

reachable(X,Y) :- link(X,Y).

reachable(X,Y) :- link(X,Z), reachable(Z,Y).

And a set of EDBs like this: link = {(a,b), (b,c), (c,c), (c,d)} The procedure for execute the evaluation is:

1. Begin by assuming all IDB relations are empty.

2. Repeatedly evaluate the rules using the EDB and the previous IDB to get a new IDB.

3. End when there is no change to IDB.