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arXiv · 2603.09558

No Cliques Allowed: The Next Step Towards BDD/FC Conjecture

Lucas Larroque·Piotr Ostropolski-Nalewaja·Michaël Thomazo
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Abstract

This paper addresses one of the fundamental open questions in the realm of existential rules: the conjecture on the finite controllability of bounded derivation depth rule sets (bdd $\Rightarrow$ fc). We take a step toward a positive resolution of this conjecture by demonstrating that universal models generated by bdd rule sets cannot contain arbitrarily large tournaments (arbitrarily directed cliques) without entailing a loop query, $\exists{x} E(x, x)$. This simple yet elegant result narrows the space of potential counterexamples to the (bdd $\Rightarrow$ fc) conjecture.

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Lucas Larroque, Piotr Ostropolski-Nalewaja, Michaël Thomazo. 2026-03-10. No Cliques Allowed: The Next Step Towards BDD/FC Conjecture. https://arxiv.org/abs/2603.09558

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