arXiv:2611.13138v1 Announce Type: new Abstract: We study Conjunctive Query Entailment Problem over ontologies con- sisting of Linear Tuple Generating Dependencies and transitivity asser- tions. A special case of this problem has been shown to be decidable in [1]. In particular, it covers the case of linear single head TGDs with bi- nary signature. In This paper we show that The problem for linear multi head TGDs with binary signature is Ackermanian hard