Markus Nissl

Lucas Berent, Markus Nissl, Emanuel Sallinger

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. We 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.

Luigi Bellomarini, Markus Nissl, Emanuel Sallinger

In this paper, we investigate finite representations of DatalogMTL models. First, we discuss sufficient conditions for detecting programs that have finite models. Then, we study infinite models that eventually become constant and introduce sufficient criteria for programs that allow for such representation. We proceed by considering infinite models that are eventually periodic and show that such representation encompasses all DatalogMTL^FP programs, a widely discussed fragment. Finally, we provide a novel algorithm for reasoning over such finite representable programs.

Markus Nissl, Emanuel Sallinger, Stefan Schulte et al.

In recent years, manifold blockchain protocols have been proposed by researchers and industrial companies alike. This has led to a very heterogeneous blockchain landscape. Accordingly, it would be desirable if blockchains could interact with each other. However, current blockchain technologies offer only limited support for interoperability, thus preventing tokens or smart contracts from leaving the scope of a particular blockchain. As a first step towards a solution for cross-chain smart contract interactions, we introduce a framework which allows to invoke a smart contract from another blockchain. We offer support for continuing a smart contract after receiving a result from a different blockchain, and for calling smart contracts recursively across blockchains. We provide a reference implementation for Ethereum-based blockchains using Solidity and evaluate the performance regarding time and cost overheads.