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Warded Datalog+- extends the logic-based language Datalog with existential quantifiers in rule heads. Existential rules are needed for advanced reasoning tasks, e.g., ontological reasoning. The theoretical efficiency guarantees of Warded Datalog+- do not cover extensions crucial for data analytics, such as arithmetic. Moreover, despite the significance of arithmetic for common data analytic scenarios, no decidable fragment of any Datalog+- language extended with arithmetic has been identified.<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2202.05086v1">arXiv:2202.05086v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dnhm5jem2resri7mvrvrm7cssa">fatcat:dnhm5jem2resri7mvrvrm7cssa</a> </span>
more »... e close this gap by defining a new language that extends Warded Datalog+- with arithmetic and prove its P-completeness. Furthermore, we present an efficient reasoning algorithm for our newly defined language and prove descriptive complexity results for a recently introduced Datalog fragment with integer arithmetic, thereby closing an open question. We lay the theoretical foundation for highly expressive Datalog+- languages that combine the power of advanced recursive rules and arithmetic while guaranteeing efficient reasoning algorithms for applications in modern AI systems, such as Knowledge Graphs.
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