Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider existential rules (aka Datalog±) as a formalism for specifying ontologies. In recent years, many classes of existential rules have been exhibited for which conjunctive query (CQ) entailment is decidable. Hover, most of these classes cannot express transitivity of binary relations, a frequently used modelling construct. ,  address the issue of whether transitivity can be safely combined with decidable classes of existential rules. First,  prove that transitivity is incompatible with one of the simplest decidable classes, namely aGRD (acyclic graph of rule dependencies), which clarifies the landscape of 'finite expansion sets' of rules. Second,  show that transitivity can be safely added to linear rules (a subclass of guarded rules, which generalizes the description logic DL-LiteR) in the case of atomic CQs, and also for general CQs if  place a minor syntactic restriction on the rule set. This is shown by means of a novel query rewriting algorithm that is specially tailored to handle transitivity rules. Third, for the identified decidable cases,  pinpoint the combined and data complexities of query entailment.
['Jean-François Baget', 'Meghyn Bienvenu', 'Marie-Laure Mugnier', 'Swan Rocher']
I am writing a research paper on a idea Combining existential rules and transitivity: next steps
[{"from": "human", "value": "I am writing a research paper on a idea Combining existential rules and transitivity: next steps"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider existential rules (aka Datalog\u00b1) as a formalism for specifying ontologies. In recent years, many classes of existential rules have been exhibited for which conjunctive query (CQ) entailment is decidable. Hover, most of these classes cannot express transitivity of binary relations, a frequently used modelling construct. ,  address the issue of whether transitivity can be safely combined with decidable classes of existential rules. First,  prove that transitivity is incompatible with one of the simplest decidable classes, namely aGRD (acyclic graph of rule dependencies), which clarifies the landscape of 'finite expansion sets' of rules. Second,  show that transitivity can be safely added to linear rules (a subclass of guarded rules, which generalizes the description logic DL-LiteR) in the case of atomic CQs, and also for general CQs if  place a minor syntactic restriction on the rule set. This is shown by means of a novel query rewriting algorithm that is specially tailored to handle transitivity rules. Third, for the identified decidable cases,  pinpoint the combined and data complexities of query entailment."}]