Description Logics Go Second-Order -- Extending EL with Universally Quantified Concepts

The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable extensions outside first-order logic. We introduce universally quantified concepts, which take the form of variables that can be replaced with arbitrary concepts, and define two semantics of this extension. A schema semantics allows replacements of concept variables only by concepts from a particular language, giving us axiom schemata similar to modal logics. A second-order semantics allows replacement of concept variables with arbitrary subsets of the domain, which is similar to quantified predicates in second-order logic. To study the proposed semantics, we focus on the extension of the description logic $\mathcal{EL}$. We show that for a useful fragment of the extension, the conclusions entailed by the different semantics coincide, allowing us to use classical $\mathcal{EL}$ reasoning algorithms even for the second-order semantics. For a slightly smaller, but still useful, fragment, we were also able to show polynomial decidability of the extension. This fragment, in particular, can express a generalized form of role chain axioms, positive self restrictions, and some forms of (local) role-value-maps from KL-ONE, without requiring any additional constructors

From fuzzy to annotated semantic web languages

The aim of this chapter is to present a detailed, selfcontained and comprehensive account of the state of the art in representing and reasoning with fuzzy knowledge in Semantic Web Languages such as triple languages RDF/RDFS, conceptual languages of the OWL 2 family and rule languages. We further show how one may generalise them to so-called annotation domains, that cover also e.g. temporal and provenance extensions

A survey of large-scale reasoning on the Web of data

As more and more data is being generated by sensor networks, social media and organizations, the Webinterlinking this wealth of information becomes more complex. This is particularly true for the so-calledWeb of Data, in which data is semantically enriched and interlinked using ontologies. In this large anduncoordinated environment, reasoning can be used to check the consistency of the data and of asso-ciated ontologies, or to infer logical consequences which, in turn, can be used to obtain new insightsfrom the data. However, reasoning approaches need to be scalable in order to enable reasoning over theentire Web of Data. To address this problem, several high-performance reasoning systems, whichmainly implement distributed or parallel algorithms, have been proposed in the last few years. Thesesystems differ significantly; for instance in terms of reasoning expressivity, computational propertiessuch as completeness, or reasoning objectives. In order to provide afirst complete overview of thefield,this paper reports a systematic review of such scalable reasoning approaches over various ontologicallanguages, reporting details about the methods and over the conducted experiments. We highlight theshortcomings of these approaches and discuss some of the open problems related to performing scalablereasoning

On the KLM properties of a fuzzy DL with Typicality

The paper investigates the properties of a fuzzy logic of typicality. The extension of fuzzy logic with a typicality operator was proposed in recent work to define a fuzzy multipreference semantics for Multilayer Perceptrons, by regarding the deep neural network as a conditional knowledge base. In this paper, we study its properties. First, a monotonic extension of a fuzzy ALC with typicality is considered (called ALC^FT) and a reformulation the KLM properties of a preferential consequence relation for this logic is devised. Most of the properties are satisfied, depending on the reformulation and on the fuzzy combination functions considered. We then strengthen ALC^FT with a closure construction by introducing a notion of faithful model of a weighted knowledge base, which generalizes the notion of coherent model of a conditional knowledge base previously introduced, and we study its properties.Comment: 15 page

Optimal Fixed-Premise Repairs of EL TBoxes: Extended Version

Reasoners can be used to derive implicit consequences from an ontology. Sometimes unwanted consequences are revealed, indicating errors or privacy-sensitive information, and the ontology needs to be appropriately repaired. The classical approach is to remove just enough axioms such that the unwanted consequences vanish. However, this is often too rough since mere axiom deletion also erases many other consequences that might actually be desired. The goal should not be to remove a minimal number of axioms but to modify the ontology such that only a minimal number of consequences is removed, including the unwanted ones. Specifically, a repair should rather be logically entailed by the input ontology, instead of being a subset. To this end, we introduce a framework for computing fixed-premise repairs of $\mathcal{EL}$ TBoxes. In the first variant the conclusions must be generalizations of those in the input TBox, while in the second variant no such restriction is imposed. In both variants, every repair is entailed by an optimal one and, up to equivalence, the set of all optimal repairs can be computed in exponential time. A prototypical implementation is provided. In addition, we show new complexity results regarding gentle repairs.This is an extended version of an article accepted at the 45th German Conference on Artificial Intelligence (KI 2022)

A survey of current, stand-alone OWL Reasoners

Abstract. We present a survey of the current OWL reasoner landscape. Through literature and web search we have identified 35 OWL reasoners that are, at least to some degree, actively maintained. We conducted a survey directly addressing the respective developers, and collected 33 responses. We present an analysis of the survey, characterising all reasoners across a wide range of categories such as supported expressiveness and reasoning services. We will also provide some insight about ongoing research efforts and a rough categorisation of reasoner calculi