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.

翻译：本文探讨存在性规则领域中的一个基本开放性问题：关于有界推导深度规则集有限可控性的猜想（bdd $\Rightarrow$ fc）。通过证明由bdd规则集生成的通用模型若包含任意大规模竞赛图（任意有向团簇），则必然蕴含循环查询$\exists{x} E(x, x)$，我们朝着该猜想的正向解决迈出了关键一步。这一简洁而精妙的结论显著缩小了可能证伪（bdd $\Rightarrow$ fc）猜想的反例空间。