Jianfeng Du

Extending description logics with uncertainty reasoning in possibilistic logic

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.

Computing minimum cost diagnoses to repair populated DL-based ontologies

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.

Towards Practical ABox Abduction in Large Description Logic Ontologies

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.

Goal-Directed Module Extraction for Explaining OWL DL Entailments

Module extraction methods have proved to be effective in improving the performance of some ontology reasoning tasks, including finding justifications to explain why an entailment holds in an OWL DL ontology. However, the existing module extraction methods that compute a syntactic locality-based module for the sub-concept in a subsumption entailment, though ensuring the resulting module to preserve all justifications of the entailment, may be insufficient in improving the performance of finding all justifications. This is because a syntactic locality-based module is independent of the super-concept in a subsumption entailment and always contains all concept/role assertions. In order to extract smaller modules to further optimize finding all justifications in an OWL DL ontology, we propose a goal-directed method for extracting a module that preserves all justifications of a given entailment. Experimental results on large ontologies show that a module extracted by our method is smaller than the corresponding syntactic locality-based module, making the subsequent computation of all justifications more scalable and more efficient.

PossDL — a possibilistic DL reasoner for uncertainty reasoning and inconsistency handling

Uncertainty reasoning and inconsistency handling are two important problems that often occur in the applications of the Semantic Web. Possibilistic description logics provide a flexible framework for representing and reasoning with ontologies where uncertain and/or inconsistent information exists. Based on our previous work, we develop a possibilistic description logic reasoner. Our demo will illustrate functionalities of our reasoner for various reasoning tasks that possibilistic description logics can provide.

A new matchmaking approach based on abductive conjunctive query answering

To perform matchmaking in Web-based scenarios where data are often incomplete, we propose an extended conjunctive query answering (CQA) problem, called abductive CQA problem, in Description Logic ontologies. Given a consistent ontology and a conjunctive query, the abductive CQA problem computes all abductive answers to the query in the ontology. An abductive answer is an answer to the query in some consistent ontology enlarged from the given one by adding a bounded number of individual assertions, where the individual assertions that can be added are confined by user-specified concept or role names. We also propose a new approach to matchmaking based on the abductive CQA semantics, in which offer information is expressed as individual assertions, request information is expressed as conjunctive queries, and matches for a request are defined as abductive answers to a conjunctive query that expresses the request. We propose a sound and complete method for computing all abductive answers to a conjunctive query in an ontology expressed in the Description Logic Program fragment of OWL 2 DL with the Unique Name Assumption. The feasibility of this method is demonstrated by a real-life application, rental matchmaking, which handles requests for renting houses.

A Decomposition-Based Approach to OWL DL Ontology Diagnosis

Computing all diagnoses of an inconsistent ontology is important in ontology-based applications. However, the number of diagnoses can be very large. It is impractical to enumerate all diagnoses before identifying the target one to render the ontology consistent. Hence, we propose to represent all diagnoses by multiple sets of partial diagnoses, where the total number of partial diagnoses can be small and the target diagnosis can be directly retrieved from these partial diagnoses. We also propose methods for computing the new representation of all diagnoses in an OWL DL ontology. Experimental results show that computing the new representation of all diagnoses is much easier than directly computing all diagnoses.

A Practical Fine-grained Approach to Resolving Incoherent OWL 2 DL Terminologies

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.

Lexicographical Inference over Inconsistent DL-Based Ontologies

Logical inconsistency may often occur throughout the development stage of a DL-based ontology. We apply the lexicographic inference to reason over inconsistent DL-based ontologies without repairing them first. We address the problem of checking consequences in a

A Decomposition-Based Approach to Optimizing Conjunctive Query Answering in OWL DL

\mathcal{SHIQ}