On the Relationship between Shy and Warded Datalog+/-

Recent years witnessed a rising interest towards Datalog-based ontological reasoning systems, both in academia and industry. These systems adopt languages, namely, fragments, that extend Datalog with existential quantification, an essential feature for reasoning. Such fragments are often shared under the collective name of Datalog$^\pm$. As ontological reasoning in the presence of existential quantification is undecidable, each fragment introduces specific syntactic limitations to achieve a good trade-off between expressive power and computational complexity. From an implementation perspective, modern reasoners borrow the vast experience of the database community in developing streaming-based data processing systems, such as volcano-iterator architectures, that sustain a limited memory footprint and good scalability. In this paper, we focus on two extremely promising, expressive, and tractable fragments, namely, Shy and Warded Datalog$^\pm$. We leverage their theoretical underpinnings to introduce novel reasoning techniques, technically, ``chase variants'', that are particularly fit for efficient reasoning in streaming-based architectures. We bridge the theoretical foundations and the reasoning algorithms with the necessary theory bases, implement the chase variants in Vadalog, our reference streaming-based engine, and efficiently solve generic ontological reasoning tasks over real-world settings.