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Warded Datalog+- extends the logic-based language Datalog with existentialquantifiers in rule heads. Existential rules are needed for advanced reasoningtasks, e.g., ontological reasoning. The theoretical efficiency guarantees ofWarded Datalog+- do not cover extensions crucial for data analytics, such asarithmetic. Moreover, despite the significance of arithmetic for common dataanalytic scenarios, no decidable fragment of any Datalog+- language extendedwith arithmetic has been identified. We close this gap by defining a newlanguage that extends Warded Datalog+- with arithmetic and prove itsP-completeness. Furthermore, we present an efficient reasoning algorithm forour newly defined language and prove descriptive complexity results for arecently introduced Datalog fragment with integer arithmetic, thereby closingan open question. We lay the theoretical foundation for highly expressiveDatalog+- languages that combine the power of advanced recursive rules andarithmetic while guaranteeing efficient reasoning algorithms for applicationsin modern AI systems, such as Knowledge Graphs.

Complexity of Arithmetic in Warded Datalog+-