A New Finitely Controllable Class of Tuple Generating Dependencies: The Triangularly-Guarded Class

In the classical database management systems (DBMS) setting, a query Q is evaluated against a database D. However, it has come to the attention of the database community the necessity to also include ontological reasoning and description logics (DLs) along with standard database techniques (Calvanese et al. 2007). As such, the ontological database management systems (ODBMS) has arised. In ODBMS, the classical database is enhanced with an ontology (Baader et al. 2016) in the form of logical assertions that generate new intensional knowledge. An expressive form of such logical assertions is the so-called tuplegenerating dependencies (TGDs), i.e., Horn rules extended by allowing existential quantifiers to appear in the rule heads (Cabibbo 1998; Patel-Schneider and Horrocks 2007; Calì, Gottlob, and Lukasiewicz 2009). Queries are evaluated against a database D and set of TGDs Σ (i.e., D Σ) rather than just D, as in the classical setting. Since for a given database D, a set Σ of TGDs, and a conjunctive query Q, the problem of determining if D Σ Q, i.e., the conjunctive query answering (CQ-Ans) problem, is undecidable in general (Beeri and Vardi 1981; Baget et al. 2011; Rosati 2011; Calì, Gottlob, and Pieris 2012; Calì, Gottlob, and Kifer 2013), a major research effort has been put forth to identifying syntactic conditions on TGDs for which CQ-Ans is decidable.