Do you handle incremental changes to the input data? Because that's the major selling point of DDlog: low-latency responses to changes in inputs.

We don't do this right now - optimising for incremental changes is actually better done by maintaining forward-chaining inferences (like the OP) rather than backward chaining, and then invalidating and updating just the inferences that have modified dependencies. Which you want depends on use case often: if you have often changing data backward chaining is generally better, but if it's largely static you can get large performance wins by materialising all the inferences, once, via forward-chaining.

Isn’t datalog with backward chaining just prolog? Datalog was known for forward chaining (bottom up) while prolog was known for backward chaining, datalog with backward chaining sounds like a misnomer.

You're not wrong - the other big difference between datalog and prolog is that datalog is a subset of prolog's functionality that enables forward-chaining to be safe (gets trickier with negation for example). I was mostly referring to the fact that Graql implements datalog semantics/capabilities, plus negation - but the execution strategy is backward-chaining.