A Set-theoretic Approach to Reasoning Services for the Description Logic 𝒟 ℒ D 4,×

In this paper we consider the most common TBox and ABox reasoning services for the description logic 𝒟ℒ〈4LQSR,x〉(D) ( 𝒟 ℒ D 4,× , for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment 4LQSR. 𝒟 ℒ D 4,× is a very expressive description logic. It combines the high scalability and efficiency of rule languages such as the SemanticWeb Rule Language (SWRL) with the expressivity of description logics. In fact, among other features, it supports Boolean operations on concepts and roles, role constructs such as the product of concepts and role chains on the left-hand side of inclusion axioms, role properties such as transitivity, symmetry, reflexivity, and irreflexivity, and data types. We further provide a KE-tableau-based procedure that allows one to reason on the main TBox and ABox reasoning tasks for the description logic 𝒟 ℒ D 4,× . Our algorithm is based on a variant of the KE-tableau system for sets of universally quantified clauses, where the KE-elimination rule is generalized in such a way as to incorporate the γ-rule. The novel system, called KEγ-tableau, turns out to be an improvement of the system introduced in [1] and of standard first-order KE-tableaux [2]. Suitable benchmark test sets executed on C++ implementations of the three mentioned systems show that in several cases the performances of the KEγ-tableau-based reasoner are up to about 400% better than the ones of the other two systems.

Model-theoretic Characterizations of Existential Rule Languages

Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep understanding of these languages in model theory, we establish model-theoretic characterizations for a number of existential rule languages such as (disjunctive) embedded dependencies, tuple-generating dependencies (TGDs), (frontier-)guarded TGDs and linear TGDs. All these characterizations hold for the class of arbitrary structures, and most of them also work on the class of finite structures. As a natural application of these results, complexity bounds for the rewritability of above languages are also identified.

Explanations for Negative Query Answers under Existential Rules

Ontology-mediated query answering is an extensively studied paradigm, where the conceptual knowledge provided by an ontology is leveraged towards more enhanced querying of data sources. A major advantage of ontological reasoning is its interpretability, which allows one to derive explanations for query answers. Indeed, explanations have a long history in knowledge representation, and have also been investigated for ontology languages based on description logics and existential rules. Existing works on existential rules, however, merely focus on understanding why a query is entailed, i.e., explaining positive query answers. In this paper, we continue this line of research and address another important problem, namely, explaining why a query is not entailed under existential rules, i.e., explaining negative query answers. We consider various problems related to explaining non-entailments from the abduction literature, and also introduce new problems. For all considered problems, we give a detailed complexity analysis for a wide range of existential rule languages and complexity measures.

Preference-based Inconsistency-Tolerant Query Answering under Existential Rules

Query answering over inconsistent knowledge bases is a problem that has attracted a great deal of interest over the years. Different inconsistency-tolerant semantics have been proposed, and most of them are based on the notion of repair, that is, a "maximal" consistent subset of the database. In general, there can be several repairs, so it is often natural and desirable to express preferences among them. In this paper, we propose a framework for querying inconsistent knowledge bases under user preferences for existential rule languages. We provide generalizations of popular inconsistency-tolerant semantics taking preferences into account and study the data and combined complexity of different relevant problems.

Explanations for Inconsistency-Tolerant Query Answering under Existential Rules

Querying inconsistent knowledge bases is a problem that has attracted a great deal of interest over the last decades. While several semantics of query answering have been proposed, and their complexity is rather well-understood, little attention has been paid to the problem of explaining query answers. Explainability has recently become a prominent problem in different areas of AI. In particular, explaining query answers allows users to understand not only what is entailed by an inconsistent knowledge base, but also why. In this paper, we address the problem of explaining query answers for existential rules under three popular inconsistency-tolerant semantics, namely, the ABox repair, the intersection of repairs, and the intersection of closed repairs semantics. We provide a thorough complexity analysis for a wide range of existential rule languages and for different complexity measures.

Ontology–based access to temporal data with Ontop: A framework proposal

Predictive analysis gradually gains importance in industry. For instance, service engineers at Siemens diagnostic centres unveil hidden knowledge in huge amounts of historical sensor data and use it to improve the predictive systems analysing live data. Currently, the analysis is usually done using data-dependent rules that are specific to individual sensors and equipment. This dependence poses significant challenges in rule authoring, reuse, and maintenance by engineers. One solution to this problem is to employ ontology-based data access (OBDA), which provides a conceptual view of data via an ontology. However, classical OBDA systems do not support access to temporal data and reasoning over it. To address this issue, we propose a framework for temporal OBDA. In this framework, we use extended mapping languages to extract information about temporal events in the RDF format, classical ontology and rule languages to reflect static information, as well as a temporal rule language to describe events. We also propose a SPARQL-based query language for retrieving temporal information and, finally, an architecture of system implementation extending the state-of-the-art OBDA platform Ontop.