  In ontology-based data access (OBDA), the classical database is enhanced with
an ontology in the form of logical assertions generating new intensional
knowledge. A powerful form of such logical assertions is the tuple-generating
dependencies (TGDs), also called existential rules, where Horn rules are
extended by allowing existential quantifiers to appear in the rule heads. In
this paper we introduce a new language called loop restricted (LR) TGDs
(existential rules), which are TGDs with certain restrictions on the loops
embedded in the underlying rule set. We study the complexity of this new
language. We show that the conjunctive query answering (CQA) under the LR TGDs
is decid- able. In particular, we prove that this language satisfies the
so-called bounded derivation-depth prop- erty (BDDP), which implies that the
CQA is first-order rewritable, and its data complexity is in AC0 . We also
prove that the combined complexity of the CQA is EXPTIME complete, while the
language membership is PSPACE complete. Then we extend the LR TGDs language to
the generalised loop restricted (GLR) TGDs language, and prove that this class
of TGDs still remains to be first-order rewritable and properly contains most
of other first-order rewritable TGDs classes discovered in the literature so
far.
