I have been working on a framework for encoding directed graphs incrementally with O(1) reachability queries, and a question emerged that I would like to think through with people who know Prolog’s foundations well.
Prolog’s negation-as-failure was arguably the first time negation was treated as a prime computational object. The limitation is well known: NAF produces a contentless result. The search tree is exhausted and failure is reported, but the negation carries no witness.
In a triordinal-encoded knowledge base—where reachability is confirmed only by unanimous positional consensus across three mutually constraining orderings—a dissent is not a search failure. It is a geometric fact, a positive certificate that the path does not exist, readable in O(1) directly from the encoding. Negation would acquire content.
There is a structural consequence beyond performance. A tree-structured knowledge base cannot represent cross-cutting relationships without duplication or loss. A directed-graph encoding handles these natively.
I am looking for discussion partners who find this direction interesting. A feature overview of the framework is at: https://doi.org/10.5281/zenodo.19480474
Enis Olgac enis@digraphs.info