Knowledge graph completion (KGC) aims to infer missing facts from existing facts. Learning logical rules plays a pivotal role in KGC, as logical rules excel in explaining why a missing fact is inferred. Most existing rule learning methods focus merely on learning chain-like rules, neglecting type constraints on entities. In practice, type constraints are crucial in expressing precise rules. Therefore, we propose a novel formalism for logical rules named TC-rules, which complements chain-like rules with both explicit and implicit type constraints on entity variables. Accordingly, we propose an end-to-end approach to effectively learn TC-rules, by parameterizing a neural model to simulate the inference of TC-rules. Considering that existing end-to-end methods learn two different sets of logical rules to respectively answer a head query (?,rnew, t) and a tail query (h,rrnew, ?), leading to confusing explanations for supporting a new fact (h,rnew, t), we propose a bi-directional learning mechanism to ensure that the TC-rules learnt for answering (?,rnew, t) are the same as the TC-rules learnt for answering (h,rnew, ?). Experimental results on eight benchmark datasets demonstrate that the proposed method outperforms state-of-the-art rule learners in both the link prediction task and the triple classification task. Furthermore, our case study confirms that expressive TC-rules can be extracted from the parameter assignment of the learnt neural model.

Ontology-mediated data access and management systems are rapidly emerging. Besides standard query answering, there is also a need for such systems to be coupled with explanation facilities, in particular to explain missing query answers (i.e. desired answers of a query which are not derivable from the given ontology and data). This support is highly demanded for debugging and maintenance of big data, and both theoretical results and algorithms proposed. However, existing query explanation algorithms either cannot scale over relative large data sets or are not guaranteed to compute all desired explanations. To the best of our knowledge, no existing algorithm can efficiently and completely explain conjunctive queries (CQs) w.r.t. ELH1 ontologies. In this paper, we present a hybrid approach to achieve this. An implementation of the proposed query explanation algorithm has been developed using an off-the-shelf Prolog engine and a datalog engine. Finally, the system is evaluated over practical ontologies. Experimental results show that our system scales over large data sets.

Computing all ABox repairs is a key to cautious or brave reasoning over inconsistent description logic (DL) ontologies. However, the number of ABox repairs can be exponential in the number of assertions in the ABox even for very lightweight DLs. Hence we propose to compute a minimal representative set of ABox repairs. A set of ABox repairs is representative, if every assertion occurring in at least one ABox repair also occurs in at least one element of this set, while every assertion occurring in all ABox repairs occurs in all elements of this set. Cautious or brave reasoning then can be approximated by standard reasoning over a minimal representative set other than the complete set of ABox repairs. However, computing a minimal representative set of ABox repairs is still intractable in general. To guarantee the tractability in data complexity for computing a minimal representative set, we focus on a class of DL ontologies called the first-order rewritable class. We propose a tractable method for computing a minimal representative set of ABox repairs in an inconsistent first-order rewritable ontology. Experimental results demonstrate the high efficiency and scalability of the proposed method.

Resolving incoherent terminologies is an important task in the maintenance of evolving OWL 2 DL ontologies. Existing approaches to this task are either semi-automatic or based on simple deletion of axioms. There is a need of fine-grained approaches to automatize this task. Since a fine-grained approach should consider multiple choices for modifying an axiom other than the deletion of axioms only, the primary challenges for developing such an approach lie in both the semantics of the repaired results and the efficiency in computing the repaired results. To tackle these challenges, we first introduce the notion of fine-grained repair based on modifying one axiom to zero or more axioms, then propose an efficient incremental method for computing all fine-grained repairs one by one. We also propose a modification function for axioms expressed in OWL 2 DL, which returns weaker axioms. Based on this modification function and the method for computing fine-grained repairs, we develop an automatic approach to resolving incoherent OWL 2 DL terminologies. Our extensive experimental results demonstrate that the proposed approach is efficient and practical.

In order to directly reason over inconsistent OWL 2 DL ontologies, this paper considers linear order inference which comes from propositional logic. Consequences of this inference in an inconsistent ontology are defined as consequences in a certain consistent sub-ontology. This paper proposes a novel framework for compiling an OWL 2 DL ontology to a Horn propositional program so that the intended consistent sub-ontology for linear order inference can be approximated from the compiled result in polynomial time. A tractable method is proposed to realize this framework. It guarantees that the compiled result has a polynomial size. Experimental results show that the proposed method computes the exact intended sub-ontology for almost all test cases, while it is significantly more efficient and scalable than state-of-the-art exact methods.

ABox abduction is an important reasoning facility in Description Logics (DLs). It finds all minimal sets of ABox axioms, called abductive solutions, which should be added to a background ontology to enforce entailment of an observation which is a specified set of ABox axioms. However, ABox abduction is far from practical by now because there lack feasible methods working in finite time for expressive DLs. To pave a way to practical ABox abduction, this paper proposes a new problem for ABox abduction and a new method for computing abductive solutions accordingly. The proposed problem guarantees finite number of abductive solutions. The proposed method works in finite time for a very expressive DL, , which underpins the W3C standard language OWL 2, and guarantees soundness and conditional completeness of computed results. Experimental results on benchmark ontologies show that the method is feasible and can scale to large ABoxes.

Finding all justifications of an OWL entailment is an important reasoning service for explaining logical inconsistencies. In this paper, we consider finding all justifications of an entailment in OWL pD* fragment, which is a fragment of OWL that makes possible decidable rule extensions of OWL. We first propose a novel approach to find all justifications of OWL pD* entailments using TMS and show the complexity of this approach. This approach is limited by the hardware capabilities of standalone systems. In order to improve its scalability to handle large scale semantic data, we optimize the proposed approach by exploiting the MapReduce technology. We implement our approach and the optimization, and do experiments on synthetic and real world data sets. Evaluation results show that our approach has the ability to scale to more than one billion triples.

Possibilistic logic provides a convenient tool for dealing with uncertainty and handling inconsistency. In this paper, we propose possibilistic description logics as an extension of description logics, which are a family of well-known ontology languages. We first give the syntax and semantics of possibilistic description logics and define several inference services in possibilistic description logics. We show that these inference serviced can be reduced to the task of computing the inconsistency degree of a knowledge base in possibilistic description logics. Since possibilistic inference services suffer from the drowning problem, that is, axioms whose confidence degrees are less than or equal to the inconsistency are not used, we consider a drowning-free variant of possibilistic inference, called linear order inference. We propose an algorithm for computing the inconsistency degree of a possibilistic description logic knowledge base and an algorithm for the linear order inference. We consider the impact of our possibilistic description logics on ontology learning and ontology merging. Finally, we implement these algorithms and provide some interesting evaluation results. © 2011 Wiley Periodicals, Inc.

Ontology population is prone to cause inconsistency because the populating process is imprecise or the populated data may conflict with the original data. By assuming that the intensional part of the populated DL-based ontology is fixed and each removable ABox assertion is given a removal cost, we repair the ontology by deleting a subset of removable ABox assertions in which the sum of removal costs is minimum. We call such subset a minimum cost diagnosis. We show that, unless P=NP, the problem of finding a minimum cost diagnosis for a DL-Lite ontology is insolvable in PTIME w.r.t. data complexity. In spite of that, we present a feasible computational method for more general (i.e. SHIQ) ontologies. It transforms a SHIQ ontology to a set of disjoint propositional programs, thus reducing the original problem into a set of independent subproblems. Each such subproblem computes an optimal model and is solvable in logarithmic calls to a SAT solver. Experimental results show that the method can handle moderately complex ontologies with over thousands of ABox assertions, where all ABox assertions can be assumed removable.