EA://INTEL — Why Confluence is Undecidable for Graphs and What Replaces Normalization

If you try to prove two structures are equivalent by forcing every graph into a single standard shape and then comparing them, the method breaks. This is not just an implementation hurdle; it is a fundamental logical barrier where joinability of critical pairs fails to guarantee confluence. In systems based on term rewriting or tree structures, we can usually normalize and check equality that way. But when the data model shifts to graphs with shared nodes and cycles, the standard route collapses because general confluence for terminating DPO graph rewriting is undecidable.

We encountered this exact dead end in a recorded failure logged as F-011. The assumption was that normalization over GIR would remain tractable, but the proof does not carry over to graphs without exploiting a specific architecture where a tree spine exists alongside the graph edges or adopting DPO-with-Interfaces where confluence becomes decidable. If we ignore this, we might proceed with an IR or evaluator that cannot reliably decide equivalence for a broad class of inputs. The fix requires choosing a different decision procedure before further investment in infrastructure work.

The question now is whether meaning-space can be stabilized if we stop relying on global normal forms for general graph structures and instead rely on properties that are decidable within the admissible region.