Cryptographic devices are sensitive to side-channel attacks, which inevitably leak electromagnetic radiation, power consumption, time, and other physical information during execution. The side-channel storage vulnerability caused by storage instructions has become one of the main targets for attackers, posing a serious threat to the implementation security of cryptographic algorithms. In this paper, following revealing the essence of the side-channel storage vulnerability at the computer architecture level, two novel technologies, by reducing the correlation between the processed data and emissions, are proposed to defend such attacks, namely the randomizing Hamming weight scheme and the balancing Hamming weight scheme. Furthermore, we apply the proposed scheme to AES and CRYSTALS-Kyber on the Cortex-M4 CPU. The experimental results show that this strategy can effectively eliminate the side-channel storage vulnerability at a low cost of time and space, thereby ensuring the secure implementation of cryptographic algorithms.

As the sole NIST-standardized quantum-resistant key encapsulation mechanism, CRYSTALS-Kyber demands rigorous scrutiny of its side-channel countermeasures. However, there is a lack of research on side-channel security for the message decoding module in masked CRYSTALS-Kyber. In this paper, we seek to address this gap. First, we conduct a side-channel security evaluation of the first-order masked message decoding function in mkm4 of CRYSTALS-Kyber, finding that an incremental storage vulnerability still exists. Then, we implement a practical experiment in the Cortex-M4 CPU using the sum-of-squared difference method, with the accuracy of the message recovery reaching 90.6% and the secret key recovery achieving 77.2%. Furthermore, we theoretically analyze that any order of masking strategy cannot effectively protect the message decoding function, except by increasing the attack difficulty to a limited extent. We also provide our idea for solving this problem by emulating the data behavior of the dual-rail pre-charge logic circuit at the software level, which can effectively ensure the implementation security of CRYSTALS-Kyber.

It is important to automatically discover the underlying tree-structured formulae from large amounts of data. In this paper, we examine learning linear temporal logic on finite traces (LTLf) formulae, which is a tree structure syntactically and characterizes temporal properties semantically. Its core challenge is to bridge the gap between the concise tree-structured syntax and the complex LTLf semantics. Besides, the learning quality is endangered by explosion of the search space and wrong search bias guided by imperfect data. We tackle these challenges by proposing an LTLf encoding method to parameterize a neural network so that the neural computation is able to simulate the inference of LTLf formulae. We first identify faithful LTLf encoding, a subclass of LTLf encoding, which has a one-to-one correspondence to LTLf formulae. Faithful encoding guarantees that the learned parameter assignment of the neural network can directly be interpreted to an LTLf formula. With such an encoding method, we then propose an end-to-end approach, TLTLf, to learn LTLf formulae through neural networks parameterized by our LTLf encoding method. Experimental results demonstrate that our approach achieves state-of-the-art performance with up to 7% improvement in accuracy, highlighting the benefits of introducing the faithful LTLf encoding.

Document-level relation extraction (DocRE)aims to extract relations between entities in a whole document.One of the pivotal challenges of DocRE is to capture the intricate interdependencies between relations of entity pairs.Previous methods have shown that logical rules can explicitly help capture such interdependencies.These methods either learn logical rules to refine the output of a trained DocRE model, or first learn logical rules from annotated data and then inject the learnt rules into a DocRE model using an auxiliary training objective.However, these learning pipelines may suffer from the issue of error propagation.To mitigate this issue, we propose Joint Modeling Relation extraction and Logical rules or JMRL for short, a novel rule-based framework that jointly learns both a DocRE model and logical rules in an endto-end fashion.Specifically, we parameterize a rule reasoning module in JMRL to simulate the inference of logical rules, thereby explicitly modeling the reasoning process.We also introduce an auxiliary loss and a residual connection mechanism in JMRL to better reconcile the DocRE model and the rule reasoning module.Experimental results on four benchmark datasets demonstrate that our proposed JMRL framework is consistently superior to existing rule-based frameworks, improving five baseline models for DocRE by a significant margin.

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.

Linear temporal logic (LTL) satisfiability checking has a high complexity, i.e., PSPACE-complete. Recently, neural networks have been shown to be promising in approximately checking LTL satisfiability in polynomial time. However, there is still a lack of neural network-based approach to the problem of checking LTL satisfiability and generating traces as evidence, simply called SAT-and-GET, where a satisfiable trace is generated as evidence if the given LTL formula is detected to be satisfiable. In this paper, we tackle SAT-and-GET via bridging LTL trace checking to neural network inference. Our key theoretical contribution is to show that a well-designed neural inference process, named after neural trace checking, is able to simulate LTL trace checking. We present a neural network-based approach VSCNet. Relying on the differentiable neural trace checking, VSCNet is able to learn both to check satisfiability and to generate traces via gradient descent. Experimental results confirm the effectiveness of VSCNet, showing that it significantly outperforms the state-of-the-art (SOTA) neural network-based approaches for trace generation, on average achieving up to 41.68% improvement in semantic accuracy. Besides, compared with the SOTA logic-based approach nuXmv and Aalta, VSCNet achieves averagely 186X and 3541X speedups on large-scale datasets, respectively.

We study the problem of learning a single occurrence regular expression with interleaving (SOIRE) from a set of text strings possibly with noise. SOIRE fully supports interleaving and covers a large portion of regular expressions used in practice. Learning SOIREs is challenging because it requires heavy computation and text strings usually contain noise in practice. Most of the previous studies only learn restricted SOIREs and are not robust on noisy data. To tackle these issues, we propose a noise-tolerant differentiable learning approach SOIREDL for SOIRE. We design a neural network to simulate SOIRE matching and theoretically prove that certain assignments of the set of parameters learnt by the neural network, called faithful encodings, are one-to-one corresponding to SOIREs for a bounded size. Based on this correspondence, we interpret the target SOIRE from an assignment of the set of parameters of the neural network by exploring the nearest faithful encodings. Experimental results show that SOIREDL outperforms the state-of-the-art approaches, especially on noisy data.

With the superior learning ability of neural networks, it is promising to obtain highly confident results for linear temporal logic (LTL) satisfiability checking in polynomial time. However, existing neural approaches are limited in inductive ability and in supporting with an arbitrary number of atomic propositions. Besides, there is no mechanism to verify the results for satisfiability checking. In this paper, we propose an approach to checking the satisfiability of an LTL formula and meanwhile generating a satisfiable trace if the LTL formula is satisfiable, where the satisfiable trace verifies the satisfiability result. The core contribution is a new graph representation for LTL formulae - one-step unfolded graph (OSUG) to incorporate the syntax and semantic features of LTL. Preliminary results show that our approach is superior to the state-of-the-art neural approaches on synthetic datasets and confirms the effectiveness of OSUG.

Formal specifications are widely used in software testing approaches, while writing such specifications is a time-consuming job. Recently, a number of methods have been proposed to mine specifications from execution traces, typically in the form of linear temporal logic (LTL). However, existing works have the following disadvantages: (1) ignoring the negative impact of imperfect traces, which come from partial profiling, missing context information, or buggy programs; (2) relying on templates, resulting in limited expressiveness; (3) requesting negative traces, which are usually unavailable in practice. In this paper, we propose PURLTL, which is able to mine arbitrary LTL specifications from imperfect traces. To alleviate the search space explosion and the wrong search bias, we propose a neural-based method to search LTL formulae, which, intuitively, simulates LTL path checking through differentiable parameter operations. To solve the problem of lacking negative traces, we transform the problem into learning from positive and unlabeled samples, by means of data augmentation and applying positive and unlabeled learning to the training process. Experiments show that our approach surpasses the previous start-of-the-art (SOTA) approach by a large margin. Besides, the results suggest that our approach is not only robust with imperfect traces, but also does not rely on formula templates.

Learning rule-based systems plays a pivotal role in knowledge graph completion (KGC). Existing rule-based systems restrict the input of the system to structural knowledge only, which may omit some useful knowledge for reasoning, e.g., textual knowledge. In this paper, we propose a two-stage framework that imposes both structural and textual knowledge to learn rule-based systems. In the first stage, we compute a set of triples with confidence scores (called \emph{soft triples}) from a text corpus by distant supervision, where a textual entailment model with multi-instance learning is exploited to estimate whether a given triple is entailed by a set of sentences. In the second stage, these soft triples are used to learn a rule-based model for KGC. To mitigate the negative impact of noise from soft triples, we propose a new formalism for rules to be learnt, named \emph{text enhanced rules} or \emph{TE-rules} for short. To effectively learn TE-rules, we propose a neural model that simulates the inference of TE-rules. We theoretically show that any set of TE-rules can always be interpreted by a certain parameter assignment of the neural model. We introduce three new datasets to evaluate the effectiveness of our method. Experimental results demonstrate that the introduction of soft triples and TE-rules results in significant performance improvements in inductive link prediction.

Learning linear temporal logic on finite traces (LTLf) formulae aims to learn a target formula that characterizes the high-level behavior of a system from observation traces in planning. Existing approaches to learning LTLf formulae, however, can hardly learn accurate LTLf formulae from noisy data. It is challenging to design an efficient search mechanism in the large search space in form of arbitrary LTLf formulae while alleviating the wrong search bias resulting from noisy data. In this paper, we tackle this problem by bridging LTLf inference to GNN inference. Our key theoretical contribution is showing that GNN inference can simulate LTLf inference to distinguish traces. Based on our theoretical result, we design a GNN-based approach, GLTLf, which combines GNN inference and parameter interpretation to seek the target formula in the large search space. Thanks to the non-deterministic learning process of GNNs, GLTLf is able to cope with noise. We evaluate GLTLf on various datasets with noise. Our experimental results confirm the effectiveness of GNN inference in learning LTLf formulae and show that GLTLf is superior to the state-of-the-art approaches.

Cross-lingual natural language inference (XNLI) is a fundamental task in cross-lingual natural language understanding.Recently this task is commonly addressed by pre-trained cross-lingual language models.Existing methods usually enhance pre-trained language models with additional data, such as annotated parallel corpora.These additional data, however, are rare in practice, especially for low-resource languages.Inspired by recent promising results achieved by prompt-learning, this paper proposes a novel prompt-learning based framework for enhancing XNLI.It reformulates the XNLI problem to a masked language modeling problem by constructing cloze-style questions through cross-lingual templates.To enforce correspondence between different languages, the framework augments a new question for every question using a sampled template in another language and then introduces a consistency loss to make the answer probability distribution obtained from the new question as similar as possible with the corresponding distribution obtained from the original question.Experimental results on two benchmark datasets demonstrate that XNLI models enhanced by our proposed framework significantly outperform original ones under both the full-shot and few-shot cross-lingual transfer settings.

Linear temporal logic over finite traces (LTLf) satisfiability checking is a fundamental and hard (PSPACE-complete) problem in the artificial intelligence community. We explore teaching end-to-end neural networks to check satisfiability in polynomial time. It is a challenge to characterize the syntactic and semantic features of LTLf via neural networks. To tackle this challenge, we propose LTLfNet, a recursive neural network that captures syntactic features of LTLf by recursively combining the embeddings of sub-formulae. LTLfNet models permutation invariance and sequentiality in the semantics of LTLf through different aggregation mechanisms of sub-formulae. Experimental results demonstrate that LTLfNet achieves good performance in synthetic datasets and generalizes across large-scale datasets. They also show that LTLfNet is competitive with state-of-the-art symbolic approaches such as nuXmv and CDLSC.

Linear temporal logic (LTL) satisfiability checking is a fundamental and hard (PSPACE-complete) problem. In this paper, we explore checking LTL satisfiability via end-to-end learning, so that we can take only polynomial time to check LTL satisfiability. Existing approaches have shown that it is possible to leverage end-to-end neural networks to predict the Boolean satisfiability problem with performance considerably higher than random guessing. Inspired by these approaches, we study two interesting questions: can end-to-end neural networks check LTL satisfiability, and can neural networks capture the semantics of LTL? To this end, we train different neural networks for keeping three logical properties of LTL, i.e., recursive property, permutation invariance, and sequentiality. We demonstrate that neural networks can indeed capture some effective biases for checking LTL satisfiability. Besides, designing a special neural network keeping the logical properties of LTL can provide a better inductive bias. We also show the competitive results of neural networks compared with state-of-the-art approaches, i.e., nuXmv and Aalta, on large scale datasets.

Social relation extraction (SRE for short), which aims to infer the social relation between two people in daily life, has been demonstrated to be of great value in reality. Existing methods for SRE consider extracting social relation only from unimodal information such as text or image, ignoring the high coupling of multimodal information. Moreover, previous studies overlook the serious unbalance distribution on social relations. To address these issues, this paper proposes FL-MSRE, a few-shot learning based approach to extracting social relations from both texts and face images. Considering the lack of multimodal social relation datasets, this paper also presents three multimodal datasets annotated from four classical masterpieces and corresponding TV series. Inspired by the success of BERT, we propose a strong BERT based baseline to extract social relation from text only. FL-MSRE is empirically shown to outperform the baseline significantly. This demonstrates that using face images benefits text-based SRE. Further experiments also show that using two faces from different images achieves similar performance as from the same image. This means that FL-MSRE is suitable for a wide range of SRE applications where the faces of two people can only be collected from different images.

Hai Wan, Haicheng Chen, Jianfeng Du, Weilin Luo, Rongzhen Ye. Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021.

Cross-lingual natural language inference is a fundamental task in cross-lingual natural language understanding, widely addressed by neural models recently. Existing neural model based methods either align sentence embeddings between source and target languages, heavily relying on annotated parallel corpora, or exploit pre-trained cross-lingual language models that are fine-tuned on a single language and hard to transfer knowledge to another language. To resolve these limitations in existing methods, this paper proposes an adversarial training framework to enhance both pre-trained models and classical neural models for cross-lingual natural language inference. It trains on the union of data in the source language and data in the target language, learning language-invariant features to improve the inference performance. Experimental results on the XNLI benchmark demonstrate that three popular neural models enhanced by the proposed framework significantly outperform the original models.

Aspect-based sentiment analysis (ABSA) aims to detect the targets (which are composed by continuous words), aspects and sentiment polarities in text. Published datasets from SemEval-2015 and SemEval-2016 reveal that a sentiment polarity depends on both the target and the aspect. However, most of the existing methods consider predicting sentiment polarities from either targets or aspects but not from both, thus they easily make wrong predictions on sentiment polarities. In particular, where the target is implicit, i.e., it does not appear in the given text, the methods predicting sentiment polarities from targets do not work. To tackle these limitations in ABSA, this paper proposes a novel method for target-aspect-sentiment joint detection. It relies on a pre-trained language model and can capture the dependence on both targets and aspects for sentiment prediction. Experimental results on the SemEval-2015 and SemEval-2016 restaurant datasets show that the proposed method achieves a high performance in detecting target-aspect-sentiment triples even for the implicit target cases; moreover, it even outperforms the state-of-the-art methods for those subtasks of target-aspect-sentiment detection that they are competent to.

This paper proposes a validation mechanism for newly added triples in a growing knowledge graph. Given a logical theory, a knowledge graph, a text corpus, and a new triple to be validated, this mechanism computes a sorted list of explanations for the new triple to facilitate the validation of it, where an explanation, called an abductive text evidence, is a set of pairs of the form (triple, window) where appending the set of triples on the left to the knowledge graph enforces entailment of the new triple under the logical theory, while every sentence window on the right which is contained in the text corpus explains to some degree why the triple on the left is true. From the angle of practice, a special class of abductive text evidences called TEP-based abductive text evidence is proposed, which is constructed from explanation patterns seen before in the knowledge graph. Accordingly, a method for computing the complete set of TEP-based abductive text evidences is proposed. Moreover, a method for sorting abductive text evidences based on distantly supervised learning is proposed. To evaluate the proposed validation mechanism, four knowledge graphs with logical theories are constructed from the four great classical masterpieces of Chinese literature. Experimental results on these datasets demonstrate the efficiency and effectiveness of the proposed mechanism.

TBox abduction explains why an observation is not entailed by a TBox, by computing multiple sets of axioms, called explanations, such that each explanation does not entail the observation alone while appending an explanation to the TBox renders the observation entailed but does not introduce incoherence. Considering that practical explanations in TBox abduction are likely to mimic minimal explanations for TBox entailments, we introduce admissible explanations which are subsets of those justifications for the observation that are instantiated from a finite set of justification patterns. A justification pattern is obtained from a minimal set of axioms responsible for a certain atomic concept inclusion by replacing all concept (resp. role) names with concept (resp. role) variables. The number of admissible explanations is finite but can still be so large that computing all admissible explanations is impractical. Thus, we introduce a variant of subset-minimality, written ⊆ds-minimality, which prefers fresh (concept or role) names than existing names. We propose efficient methods for computing all admissible ⊆ds-minimal explanations and for computing all justification patterns, respectively. Experimental results demonstrate that combining the proposed methods is able to achieve a practical approach to TBox abduction.

ABox abduction plays an important role in reasoning over description logic (DL) ontologies. However, it does not work with inconsistent DL ontologies. To tackle this problem while achieving tractability, we generalize ABox abduction from the classical semantics to an inconsistency-tolerant semantics, namely the Intersection ABox Repair (IAR) semantics, and propose the notion of IAR-explanations in inconsistent DL ontologies. We show that computing all minimal IAR-explanations is tractable in data complexity for first-order rewritable ontologies. However, the computational method may still not be practical due to a possibly large number of minimal IAR-explanations. Hence we propose to use preference information to reduce the number of explanations to be computed.

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.

ABox abduction is an important reasoning mechanism for description logic ontologies. It computes all minimal explanations (sets of ABox assertions) whose appending to a consistent ontology enforces the entailment of an observation while keeps the ontology consistent. We focus on practical computation for a general problem of ABox abduction, called the query abduction problem, where an observation is a Boolean conjunctive query and the explanations may contain fresh individuals neither in the ontology nor in the observation. However, in this problem there can be infinitely many minimal explanations. Hence we first identify a class of TBoxes called first-order rewritable TBoxes. It guarantees the existence of finitely many minimal explanations and is sufficient for many ontology applications. To reduce the number of explanations that need to be computed, we introduce a special kind of minimal explanations called representative explanations from which all minimal explanations can be retrieved. We develop a tractable method (in data complexity) for computing all representative explanations in a consistent ontology. xperimental results demonstrate that the method is efficient and scalable for ontologies with large ABoxes.

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.

ABox abduction is an important aspect for abductive reasoning in Description Logics (DLs). It finds all minimal sets of ABox axioms that should be added to a background ontology to enforce entailment of a specified set of ABox axioms. As far as we know, by now there is only one ABox abduction method in expressive DLs computing abductive solutions with certain minimality. However, the method targets an ABox abduction problem that may have infinitely many abductive solutions and may not output an abductive solution in finite time. Hence, in this paper we propose a new ABox abduction problem which has only finitely many abductive solutions and also propose a novel method to solve it. The method reduces the original problem to an abduction problem in logic programming and solves it with Prolog engines. Experimental results show that the method is able to compute abductive solutions in benchmark OWL DL ontologies with 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.

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.

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.