One of the main challenges in the area of Neuro-Symbolic AI is to perform logical reasoning in the presence of both neural and symbolic data. This requires combining heterogeneous data sources such as knowledge graphs, neural model predictions, structured databases, crowd-sourced data, and many more. To allow for such reasoning, we generalise the standard rule-based language Datalog with existential rules (commonly referred to as tuple-generating dependencies) to the fuzzy setting, by allowing for arbitrary t-norms in the place of classical conjunctions in rule bodies. The resulting formalism allows us to perform reasoning about data associated with degrees of uncertainty while preserving computational complexity results and the applicability of reasoning techniques established for the standard Datalog setting. In particular, we provide fuzzy extensions of Datalog chases which produce fuzzy universal models and we exploit them to show that in important fragments of the language, reasoning has the same complexity as in the classical setting.

Modern data processing applications often combine information from a variety of complex sources. Oftentimes, some of these sources, like Machine-Learning systems or crowd-sourced data, are not strictly binary but associated with some degree of confidence in the observation. Ideally, reasoning over such data should take this additional information into account as much as possible. To this end, we propose extensions of Datalog and Datalog+/- to the semantics of Lukasiewicz logic Ł, one of the most common fuzzy logics. We show that such an extension preserves important properties from the classical case and how these properties can lead to efficient reasoning procedures for these new languages.

Competitor data constitutes information significantly valuable for many business applications. Meltwater provides users with access to a large Company Information System (CIS), Owler, which contains competitor pairs and other useful information about companies. Meltwater has been seeking a practical solution to discover more competitor pairs in Owler. The first attempt, a fully-manual workflow (called MW_Manual) for finding more competitor pairs in Owler consisted of two manual steps: a filtering step that excludes obvious non-competitor company pairs, and a further inspection process that inspects each left company pair after the filtering step. MW_Manual was cost prohibitive because the results of the filtering step contained too many non-competitor pairs. Inspecting such non-competitor pairs caused an overhead to the overall workload. To reduce the manual workload, especially the required human effort in the manual inspection process, Meltwater has transformed MW_Manual into a semi-automatic workflow (called MW_CPFilter) by replacing the manual filtering with an automatic yet more precise process that adopts a system called CPFilter. This paper presents CPFilter, a system used in the filtering process of MW_CPFilter. CPFilter automatically pre-computes likely competitor pairs from existing competitor pairs in Owler. CPFilter combines (i) the generation of new competitor candidate pairs by inference from existing competitors and other company-specific knowledge, with (ii) the validation of each candidate competitor pair of two companies by checking whether or not empirical evidence that indicates the competitor relationships of these two companies can be found. CPFilter has three key advantages compared with the manual filtering process and previous works: (i) it resulted in a high workload reduction rate of 0.81, (ii) it is domain-independent so that it can be applied to different sectors in Owler, and (iii) its results are explainable so that humans can easily understand its results.

Abstract Modern applications combine information from a great variety of sources. Oftentimes, some of these sources, like machine-learning systems, are not strictly binary but associated with some degree of (lack of) confidence in the observation. We propose MV-Datalog and $\mathrm{MV-Datalog}^\pm$ as extensions of Datalog and $\mathrm{Datalog}^\pm$ , respectively, to the fuzzy semantics of infinite-valued Łukasiewicz logic $\mathbf{L}$ as languages for effectively reasoning in scenarios where such uncertain observations occur. We show that the semantics of MV-Datalog exhibits similar model theoretic properties as Datalog. In particular, we show that (fuzzy) entailment can be decided via minimal fuzzy models. We show that when they exist, such minimal fuzzy models are unique and can be characterised in terms of a linear optimisation problem over the output of a fixed-point procedure. On the basis of this characterisation, we propose similar many-valued semantics for rules with existential quantification in the head, extending $\mathrm{Datalog}^\pm$ .