The connections between symbolic rules and neural networks have been explored in various directions, including rule mining through neural networks and rule-based explanation for neural networks. These approaches allow symbolic rules to be extracted from neural network models, which offers explainability to the models. However, the plausibility of the extracted rules is rarely analysed. In this paper, we show that the confidence degrees of extracted rules are generally not high, and we propose a new family of Graph Neural Networks that can be trained with the guidance of rules. Hence, the inference of our model simulates the rule reasoning. Moreover, rules with high confidence degrees can be extracted from the trained model that aligns with the inference of the model, which verifies the effectiveness of the rule guidance. Experimental evaluation of knowledge graph reasoning tasks further demonstrates the effectiveness of our model.

Complex Query Answering over incomplete knowledge graphs is a fundamental yet challenging task. Existing methods based on a pretrained knowledge graph embedding model have achieved good performance. However, they ignore logical rules. Logical rules, as part of the conceptual layer in knowledge graphs, contain rich background information that enhances logical reasoning and improves the performance of models. To address this problem, we propose a model that incorporates logical rules for complex query answering over knowledge graphs called R-CQA (Complex Query Answering with Rules). This model introduces implicit and explicit rule injection modules to the existing CQA models. The implicit rule injection module models logical rules as additional data for training and incorporates rule information into knowledge graph embedding model, which enhances inference. The explicit rule injection module uses logical rules to rewrite queries and constructs a query set for each original query, which avoids missing answers for inference. However, implicit rule injection does not really use logical rules for reasoning which decreases the interpretability and accuracy of logical rules. Explicit rule injection is influenced by the quantity and quality of logical rules. Therefore, we combine both methods to take advantage of their respective strengths. Experiments on 3 datasets demonstrate our model obtains state-of-the-art performance on complex query answering.

Logical rules have been widely used for expressing schema knowledge in various practical applications. It is infeasible to handcraft rules from large knowledge graphs (KGs) and thus many methods have been proposed for learning rules automatically from KGs. However, it is largely ignored how to extract rules in a (target) KG from rules that already exist in some other (source) KGs. In this paper, we propose a framework for KG rule learning based on transfer learning. A major challenge for establishing such a framework is that a suitable alignment mechanism is required for mapping certain subgraph structures between predicates in the source KG and the target KG. Hence, our framework provides a new method for predicate mapping based on graph-structural similarity. The proposed framework can be used as a standalone rule learner but more importantly, it paves a new way for enhancing the state-of-the-art rule learners for large KGs. Extensive experiments are conducted to evaluate the new approach to rule learning, which shows that rules in smaller KGs can be effectively transferred to a large KG.

Abstract Possibilistic logic programs (poss-programs) under stable models are a major variant of answer set programming. While its semantics (possibilistic stable models) and properties have been well investigated, the problem of inductive reasoning has not been investigated yet. This paper presents an approach to extracting poss-programs from a background program and examples (parts of intended possibilistic stable models). To this end, the notion of induction tasks is first formally defined, its properties are investigated and two algorithms ilpsm and ilpsmmin for computing induction solutions are presented. An implementation of ilpsmmin is also provided and experimental results show that when inputs are ordinary logic programs, the prototype outperforms a major inductive learning system for normal logic programs from stable models on the datasets that are randomly generated.

Multiple-choice question answering (MCQA) becomes particularly challenging when all choices are relevant to the question and are semantically similar. Yet this setting of MCQA can potentially provide valuable clues for choosing the right answer. Existing models often rank each choice separately, overlooking the context provided by other choices. Specifically, they fail to leverage the semantic commonalities and nuances among the choices for reasoning. In this paper, we propose a novel MCQA model by differentiating choices through identifying and eliminating their commonality, called DCQA. Our model captures token-level attention of each choice to the question, and separates tokens of the question attended to by all the choices (i.e., commonalities) from those by individual choices (i.e., nuances). Using the nuances as refined contexts for the choices, our model can effectively differentiate choices with subtle differences and provide justifications for choosing the correct answer. We conduct comprehensive experiments across five commonly used MCQA benchmarks, demonstrating that DCQA consistently outperforms baseline models. Furthermore, our case study illustrates the effectiveness of the approach in directing the attention of the model to more differentiating features.

In commonsense question answering (CSQA), pre-trained language models are often used to generate background knowledge that provides clues to improve the interpretability and performance of CSQA models. However, these methods are often ineffective for generating clues to distinguish similar options, and they also have limitations in using generative capabilities to solve CSQA tasks. In this paper, we propose a new model for CSQA that can differentiate the options for a question more effectively. This model leverages the generative capabilities of the pre-trained model to better understand the relationship between question and candidate options, creating clues that aid in effectively distinguishing choices for the question. Moreover, a mechanism is introduced to encourage the model to discern distinctions among options. Our proposed model demonstrates superior performance on four CSQA datasets, outperforming comparable models.

Temporal Knowledge Graphs (TKG) reasoning has emerged as a powerful methodology for prediction in various domains. Unlike traditional Knowledge Graphs(KG), TKGs introduce a critical time dimension to the graph structure. Existing TKG reasoning methods expose two important limitations. The first is they are primarily designed to predict the immediate next time step. When applied to multi-step predictions, this leads to an iterative process that compromises prediction efficiency. The second limitation is their performance often depends on short-term memory and overlook long-term global information. To overcome these limitations, we introduce the Echo State Temporal Knowledge Graph Network (ESTN), an innovative approach leveraging the Echo State Networks (ESN) for TKG reasoning. Specifically, the ESTN contains a Graph Embedder (GE) which integrates both short-term and long-term information within the TKG, enhancing the depth and accuracy of the data representation in graph latent space (embeddings). A Time Module (TM) is designed to facilitate direct prediction over multiple time steps, significantly improved the prediction efficiency. Extensive experiments demonstrate that our method not only show robust performance, but also offers an alternative approach to TKG reasoning, emphasizing how the distinct features of ESN can be effectively harnessed in TKG reasoning tasks.

Existing models for commonsense question answering (CQA) usually focus on combining pre-trained language models (PLMs) and structured knowledge graphs (KGs) for joint reasoning. However, such approaches encode a QA context (i.e., a pair of the question and a choice) separately from other choices, ineffective for explicitly capturing useful subtle differences among the choices, which results in incorrect answers in some cases. This paper proposes a novel model LNC (Learning Nuance among Choices) for addressing this problem and thus provides an improved approach to multiple-choice question answering. Specifically, LNC explicitly interacts between the text knowledge corresponding to each choice and the external KG knowledge corresponding to each choice, and removes the commonalities among similar choices, allowing the model to focus on different relevant knowledge based on the choices, thereby distinguishing semantically similar choices. Experimental results on major benchmark datasets show that LNC is competitive comparing to the baseline models.

Named entity recognition (NER) is the task of identifying and classifying named entities from texts. NER can benefit from linguistic dependency information, yet existing NER models can only utilize such information on datasets where dependency annotations are readily available. Dependency parsing (DP) models can be used to generate annotations, which are trained independent of the NER task and can cause error propagation to NER. In this paper, we propose a joint NER and DP model through multi-task learning, which allows the NER and DP modules to benefit from the joint training and provides an end-to-end solution to dependency-guided NER. Our model JOINDER uses a shared contextualized embedder, a word encoder, a biaffine dependency classifier, and a multi-hop dependency-guided NER. Experiments on several standard datasets in four languages show the effectiveness of joint learning and the outstanding performance of JOINDER compared to existing models. Moreover, our model can transfer dependency knowledge to other datasets with no dependency annotat.

Tuple-generating dependencies (TGDs or existential rules) are an expressive constraint language for ontology-mediated query answering and thus query answering is of high complexity. Existing systems based on first-order rewriting methods can lead to queries too large for DBMS to handle. It is shown that datalog rewriting can result in more compact queries, yet previously proposed datalog rewriting methods are mostly inefficient for implementation. In this paper, we fill the gap by proposing an efficient datalog rewriting approach for answering conjunctive queries over TGDs, and identify and combine existing fragments of TGDs for which our rewriting method terminates. We implemented a prototype system Drewer, and experiments show that it is able to handle a wide range of benchmarks in the literature. Moreover, Drewer shows superior performance over state-of-the-art systems on both the compactness of rewriting and the efficiency of query answering.

The relation classification is to identify semantic relations between two entities in a given text. While existing models perform well for classifying inverse relations with large datasets, their performance is significantly reduced for few-shot learning. In this paper, we propose a function words adaptively enhanced attention framework (FAEA) for few-shot inverse relation classification, in which a hybrid attention model is designed to attend class-related function words based on meta-learning. As the involvement of function words brings in significant intra-class redundancy, an adaptive message passing mechanism is introduced to capture and transfer inter-class differences.We mathematically analyze the negative impact of function words from dot-product measurement, which explains why the message passing mechanism effectively reduces the impact. Our experimental results show that FAEA outperforms strong baselines, especially the inverse relation accuracy is improved by 14.33% under 1-shot setting in FewRel1.0.

It is natural and effective to use rules for representing explicit knowledge in knowledge graphs. However, it is challenging to learn rules automatically from very large knowledge graphs such as Freebase and YAGO. This paper presents a new approach, RLvLR (Rule Learning via Learning Representations), to learning rules from large knowledge graphs by using the technique of embedding in representation learning together with a new sampling method. Based on RLvLR, a new method RLvLR-Stream is developed for learning rules from streams of knowledge graphs. Both RLvLR and RLvLR-Stream have been implemented and experiments conducted to validate the proposed methods regarding the tasks of rule learning and link prediction. Experimental results show that our systems are able to handle the task of rule learning from large knowledge graphs with high accuracy and outperform some state-of-the-art systems. Specifically, for massive knowledge graphs with hundreds of predicates and over 10M facts, RLvLR is much faster and can learn much more quality rules than major systems for rule learning in knowledge graphs such as AMIE+. In the setting of knowledge graph streams, RLvLR-Stream significantly improved RLvLR for both rule learning and link prediction.

In this paper, we study an information exchange process in which a network of individuals exchanges a binary opinion.In the process, the individuals change their opinions only if a majority of their neighbours have the opposite opinion and they do it synchronously.Motivated by applications in multiagent systems, distributed computing, and social science, our goal is to derive graphtheoretic features of the network that guarantee whenever a majority of individuals initially have the same opinion, they will eventually spread the opinion to all individuals.We tackle the problem by first introducing a graph-theoretic notion called controlling set which is capable of characterising the information exchange process and, by exploiting the notion, we obtain a series of lower and upper bounds on the in-degree of vertices as well as lower bound on the size of certain neighbourhoods for guaranteeing the majority to unanimity behaviour.

Existential rules are an expressive ontology formalism for ontology-mediated query answering and thus query answering is of high complexity, while several tractable fragments have been identified. Existing systems based on first-order rewriting methods can lead to queries too large for DBMS to handle. It is shown that datalog rewriting can result in more compact queries, yet previously proposed datalog rewriting methods are mostly inefficient for implementation. In this paper, we fill the gap by proposing an efficient datalog rewriting approach for answering conjunctive queries over existential rules, and identify and combine existing fragments of existential rules for which our rewriting method terminates. We implemented a prototype system Drewer, and experiments show that it is able to handle a wide range of benchmarks in the literature. Moreover, Drewer shows superior or comparable performance over state-of-the-art systems on both the compactness of rewriting and the efficiency of query answering.

Modal logics are primary formalisms for multi-agent systems but major reasoning tasks in such logics are intractable, which impedes applications of multi-agent modal logics such as automatic planning. One technique of tackling the intractability is to identify a fragment called a normal form of multiagent logics such that it is expressive but tractable for reasoning tasks such as entailment checking, bounded conjunction transformation and forgetting. For instance, DNF of propositional logic is tractable for these reasoning tasks. In this paper, we first introduce a notion of logical separability and then define a novel disjunctive normal form SDNF for the multiagent logic Kn, which overcomes some shortcomings of existing approaches. In particular, we show that every modal formula in Kn can be equivalently casted as a formula in SDNF, major reasoning tasks tractable in propositional DNF are also tractable in SDNF, and moreover, formulas in SDNF enjoy the property of logical separability. To demonstrate the usefulness of our approach, we apply SDNF in multi-agent epistemic planning. Finally, we extend these results to three more complex multi-agent logics Dn, K45n and KD45n.

AGM contraction and revision assume an underlying logic that contains propositional logic. Consequently, this assumption excludes many useful logics such as the Horn fragment of propositional logic and most description logics. Our goal in this paper is to generalise AGM contraction and revision to (near-)arbitrary fragments of classical first-order logic. To this end, we first define a very general logic that captures these fragments. In so doing, we make the modest assumptions that a logic contains conjunction and that information is expressed by closed formulas or sentences. The resulting logic is called first-order conjunctive logic or FC logic for short. We then take as the point of departure the AGM approach of constructing contraction functions through epistemic entrenchment, that is the entrenchment-based contraction. We redefine entrenchment-based contraction in ways that apply to any FC logic, which we call FC contraction. We prove a representation theorem showing its compliance with all the AGM contraction postulates except for the controversial recovery postulate. We also give methods for constructing revision functions through epistemic entrenchment which we call FC revision; which also apply to any FC logic. We show that if the underlying FC logic contains tautologies then FC revision complies with all the AGM revision postulates. Finally, in the context of FC logic, we provide three methods for generating revision functions via a variant of the Levi Identity, which we call contraction, withdrawal and cut generated revision, and explore the notion of revision equivalence. We show that withdrawal and cut generated revision coincide with FC revision and so does contraction generated revision under a finiteness condition.

Existential rules, a family of expressive ontology languages, inherit desired expressive and reasoning properties from both description logics and logic programming. On the other hand, forgetting is a well studied operation for ontology reuse, obfuscation and analysis. Yet it is challenging to establish a theory of forgetting for existential rules. In this paper, we lay the foundation for a theory of forgetting for existential rules by developing a novel notion of unfolding. In particular, we introduce a definition of forgetting for existential rules in terms of query answering and provide a characterisation of forgetting by the unfolding. A result of forgetting may not be expressible in existential rules, and we then capture the expressibility of forgetting by a variant of boundedness. While the expressibility is undecidable in general, we identify a decidable fragment. Finally, we provide an algorithm for forgetting in this fragment.

The pattern satisfiability is a fundamental problem for SPARQL. This paper provides a complete analysis of decidability/undecidability of satisfiability problems for SPARQL 1.1 patterns. A surprising result is the undecidability of satisfiability for SPARQL 1.1 patterns when only AND and MINUS are expressible. Also, it is shown that any fragment of SPARQL 1.1 without expressing both AND and MINUS is decidable. These results provide a guideline for future SPARQL query language design and implementation.

We study the problem of learning first-order rules from large Knowledge Graphs (KGs). With recent advancement in information extraction, vast data repositories in the KG format have been obtained such as Freebase and YAGO. However, traditional techniques for rule learning are not scalable for KGs. This paper presents a new approach RLvLR to learning rules from KGs by using the technique of embedding in representation learning together with a new sampling method. Experimental results show that our system outperforms some state-of-the-art systems. Specifically, for massive KGs with hundreds of predicates and over 10M facts, RLvLR is much faster and can learn much more quality rules than major systems for rule learning in KGs such as AMIE+. We also used the RLvLR-mined rules in an inference module to carry out the link prediction task. In this task, RLvLR outperformed Neural LP, a state-of-the-art link prediction system, in both runtime and accuracy.

Recent methods have adapted the well-established AGM and belief base frameworks for belief change to cover belief revision in logic programs. In this study here, we present two new sets of belief change operators for logic programs. They focus on preserving the explicit relationships expressed in the rules of a program, a feature that is missing in purely semantic approaches that consider programs only in their entirety. In particular, operators of the latter class fail to satisfy preservation and support, two important properties for belief change in logic programs required to ensure intuitive results. We address this shortcoming of existing approaches by introducing partial meet and ensconcement constructions for logic program belief change, which allow us to define syntax-preserving operators for satisfying preservation and support. Our work is novel in that our constructions not only preserve more information from a logic program during a change operation than existing ones, but they also facilitate natural definitions of contraction operators, the first in the field to the best of our knowledge. To evaluate the rationality of our operators, we translate the revision and contraction postulates from the AGM and belief base frameworks to the logic programming setting. We show that our operators fully comply with the belief base framework and formally state the interdefinability between our operators. We further compare our approach to two state-of-the-art logic program revision methods and demonstrate that our operators address the shortcomings of one and generalise the other method.

Two essential tasks in managing description logic knowledge bases are eliminating problematic axioms and incorporating newly formed ones. Such elimination and incorporation are formalised as the operations of contraction and revision in belief change. In this paper, we deal with contraction and revision for the DL-Lite family through a model-theoretic approach. Standard description logic semantics yields an infinite number of models for DL-Lite knowledge bases, thus it is difficult to develop algorithms for contraction and revision that involve DL models. The key to our approach is the introduction of an alternative semantics called type semantics which can replace the standard semantics in characterising the standard inference tasks of DL-Lite. Type semantics has several advantages over the standard one. It is more succinct and importantly, with a finite signature, the semantics always yields a finite number of models. We then define model-based contraction and revision functions for DL-Lite knowledge bases under type semantics and provide representation theorems for them. Finally, the finiteness and succinctness of type semantics allow us to develop tractable algorithms for instantiating the functions.

The critical behaviors of NP-complete problems have been studied extensively, and numerous results have been obtained for Boolean formula satisfiability (SAT) and constraint satisfaction (CSP), among others. However, few results are known for the critical behaviors of NP-hard nonmonotonic reasoning problems so far; in particular, a mathematical model for phase transition in nonmonotonic reasoning is still missing. In this article, we investigate the phase transition of negative two-literal logic programs under the answer-set semantics. We choose this class of logic programs since it is the simplest class for which the consistency problem of deciding if a program has an answer set is still NP-complete. We first introduce a new model, called quadratic model for generating random logic programs in this class. We then mathematically prove that the consistency problem for this class of logic programs exhibits a phase transition. Furthermore, the phase-transition follows an easy-hard-easy pattern. Given the correspondence between answer sets for negative two-literal programs and kernels for graphs, as a corollary, our result significantly generalizes de la Vega's well-known theorem for phase transition on the existence of kernels in random graphs. We also report some experimental results. Given our mathematical results, these experimental results are not really necessary. We include them here as they suggest that our phase-transition result is more general and likely holds for more general classes of logic programs.

The recent years have seen several proposals aimed at placing the revision of logic programs within the belief change frameworks established for classical logic. A crucial challenge of this task lies in the nonmonotonicity of standard logic programming semantics. Existing approaches have thus used the monotonic characterisation via SE-models to develop semantic revision operators, which however neglect any syntactic information, or reverted to a syntax-oriented belief base approach altogether. In this paper, we bridge the gap between semantic and syntactic techniques by adapting the idea of a partial meet construction from classical belief change. This type of construction allows us to define new model-based operators for revising as well as contracting logic programs that preserve the syntactic structure of the programs involved. We demonstrate the rationality of our operators by testing them against the classic AGM or alternative belief change postulates adapted to the logic programming setting. We further present an algorithm that reduces the partial meet revision or contraction of a logic program to performing revision or contraction only on the relevant subsets of that program.

In this paper, we present an approach to forgetting in disjunctive logic programs, where forgetting an atom from a program amounts to a reduction in the signature of that program. Notably, the approach is syntax-independent, so that if two programs are strongly equivalent, then the result of forgetting a given atom in each program is also strongly equivalent. Our central definition of forgetting is abstract: forgetting an atom from program P is characterised by the set of those SE consequences of P that do not mention the atom to be forgotten. We provide an equivalent, syntactic, characterization in which forgetting an atom p is given by those rules in the program that do not mention p, together with rules obtained by a single inference step from those rules that do mention p. Forgetting is shown to have appropriate properties; in particular, answer sets are preserved in forgetting an atom. As well, forgetting an atom via the syntactic characterization results in a modest (at worst quadratic) blowup in the program size. Finally, we provide a prototype implementation of this approach to forgetting.

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.

Model-based approaches provide a semantically well justified way to revise ontologies. However, in general, model-based revision operators are limited due to lack of efficient algorithms and inexpressibility of the revision results. In this paper, we make both theoretical and practical contribution to efficient computation of model-based revisions in DL-Lite. Specifically, we show that maximal approximations of two well-known model-based revisions for DL-Lite_R can be computed using a syntactic algorithm. However, such a coincidence of model-based and syntactic approaches does not hold when role functionality axioms are allowed. As a result, we identify conditions that guarantee such a coincidence for DL-Lite_FR. Our result shows that both model-based and syntactic revisions can co-exist seamlessly and the advantages of both approaches can be taken in one revision operator. Based on our theoretical results, we develop a graph-based algorithm for the revision operat

The theory of (variable) forgetting has received significant attention in nonmonotonic reasoning, especially, in answer set programming. However, the problem of establishing a theory of forgetting for some expressive nonmonotonic logics such as McCarthy's circumscription is rarely explored.In this paper a theory of forgetting for propositional circumscription is proposed, which is not a straightforward adaption of existing approaches. In particular, some properties that are essential for existing proposals do not hold any longer or have to be reformulated. Several useful properties of the new forgetting are proved, which demonstrate suitability of the forgetting for circumscription. A sound and complete algorithm for the forgetting is developed and an analysis of computational complexity is given.

The development and maintenance of large and complex ontologies are often time-consuming and error-prone. Thus, automated ontology learning and evolution have attracted intensive research interest. In data-centric applications where ontologies are designed from the data or automatically learnt from it, when new data instances are added that contradict the ontology, it is often desirable to incrementally revise the ontology according to the added data. In description logics, this problem can be intuitively formulated as the operation of TBox contraction, i.e., rational elimination of certain axioms from the logical consequences of a TBox, and it is w.r.t. an ABox. In this paper we introduce a model-theoretic approach to such a contraction problem by using an alternative semantic characterisation of DL-Lite TBoxes. We show that entailment checking (without necessarily first computing the contraction result) is in coNP, which does not shift the corresponding complexity in propositional logic, and the problem is tractable when the size of the new data is bounded.

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.

DL-Lite is an important family of description logics. Recently, there is an increasing interest in handling inconsistency in DL-Lite as the constraint imposed by a TBox can be easily violated by assertions in ABox in DL-Lite. In this paper, we present a distance-based paraconsistent semantics based on the notion of feature in DL-Lite, which provides a novel way to rationally draw meaningful conclusions even from an inconsistent knowledge base. Finally, we investigate several important logical properties of this entailment relation based on the new semantics and show its promising advantages in non-monotonic reasoning for DL-Lite.

Ontology engineering and maintenance require (semi-)automated ontology change operations. Intensive research has been conducted on TBox and ABox changes in description logics (DLs), and various change operators have been proposed in the literature. Existing operators largely fall into two categories: syntax-based and model-based. While each approach has its advantages and disadvantages, an important topic that has rarely been explored is how to achieve a balance between syntax-based and model-based approaches. Also, most existing operators are specially designed for either TBox change or ABox change, and cannot handle the general ontology revision task—given a DL knowledge base (KB, a pair consisting of a TBox and an ABox), how to revise it by a set of TBox and ABox axioms ( i.e. , a new DL KB). In this article, we introduce an alternative structure for DL-Lite, called a featured interpretation, and show that featured models provide a finite and tight characterization to the classical semantics of DL-Lite. A key issue for defining a change operator is the so-called expressibility, that is, whether a set of models (or featured models here) is axiomatizable in DLs. It is indeed much easier to obtain expressibility results for featured models than for classical DL models. As a result, the new semantics determined by featured models provides a method for defining and studying various changes of DL-Lite KBs that involve both TBoxes and ABoxes. To demonstrate the usefulness of the new semantic characterization in ontology change, we define two revision operators for DL-Lite KBs using featured models and study their properties. In particular, we show that our two operators both satisfy AGM postulates. We show that the complexity of our revisions is Π P 2 -complete, that is, on the same level as major revision operators in propositional logic, which further justifies the feasibility of our revision approach for DL-Lite. Also, we develop algorithms for these DL-Lite revisions.

Abstract This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of answer sets for a random program converges to a constant when the number of atoms approaches infinity. Several experimental results are also reported, which justify the suitability of the linear model. It is also experimentally shown that, under this model, the size distribution of answer sets for random programs tends to a normal distribution when the number of atoms is sufficiently large.

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.

Two essential tasks in managing Description Logic (DL) ontologies are eliminating problematic axioms and incorporating newly formed axioms. Such elimination and incorporation are formalised as the operations of contraction and revision in belief change.In this paper, we deal with contraction and revision for the DL-Lite family through a model-theoretic approach.Standard DL semantics yields infinite numbers of models for DL-Lite TBoxes, thus it is not practical to develop algorithms for contraction and revision that involve DL models. The key to our approach is the introduction of an alternative semantics called type semantics which is more succinct than DL semantics. More importantly, with a finite signature, type semantics always yields finite humber of models.We then define model-based contraction and revision for DL-Lite TBoxesunder type semantics and provide representation theorems for them.Finally, the succinctness of type semantics allows us to develop tractable algorithms for both operations.

The answer set semantics presented by Faber et al. [27] has been widely used to define so called FLP answer sets for different types of logic programs. However, it was recently observed that when being extended from normal to more general classes of logic programs, this approach may produce answer sets with circular justifications that are caused by self-supporting loops. The main reason for this behavior is that the FLP answer set semantics is not fully constructive by a bottom up construction of answer sets. In this paper, we overcome this problem by enhancing the FLP answer set semantics with a level mapping formalism such that every answer set I can be built by fixpoint iteration of a one-step provability operator (more precisely, an extended van Emden–Kowalski operator for the FLP reduct fΠI). This is inspired by the fact that under the standard answer set semantics, each answer set I of a normal logic program Π is obtainable by fixpoint iteration of the standard van Emden–Kowalski one-step provability operator for the Gelfond–Lifschitz reduct ΠI, which induces a level mapping. The enhanced FLP answer sets, which we call well-justified FLP answer sets, are thanks to the level mapping free of circular justifications. As a general framework, the well-justified FLP answer set semantics applies to logic programs with first-order formulas, logic programs with aggregates, description logic programs, hex-programs etc., provided that the rule satisfaction is properly extended to such general logic programs. We study in depth the computational complexity of FLP and well-justified FLP answer sets for general classes of logic programs. Our results show that the level mapping does not increase the worst-case complexity of FLP answer sets. Furthermore, we describe an implementation of the well-justified FLP answer set semantics, and report about an experimental evaluation, which indicates a potential for performance improvements by the level mapping in practice.

Forgetting is an important tool for reducing ontologies by eliminating some redundant concepts and roles while preserving sound and complete reasoning. Attempts have previously been made to address the problem of forgetting in relatively simple description logics (DLs), such as DL‐Lite and extended . However, the issue of forgetting for ontologies in more expressive DLs, such as and OWL DL, is largely unexplored. In particular, the problem of characterizing and computing forgetting for such logics is still open. In this paper, we first define semantic forgetting about concepts and roles in ontologies and state several important properties of forgetting in this setting. We then define the result of forgetting for concept descriptions in , state the properties of forgetting for concept descriptions, and present algorithms for computing the result of forgetting for concept descriptions. Unlike the case of DL‐Lite, the result of forgetting for an ontology does not exist in general, even for the special case of forgetting in TBoxes. This makes the problem of computing the result of forgetting in more challenging. We address this problem by defining a series of approximations to the result of forgetting for ontologies and studying their properties. Our algorithms for computing approximations can be directly implemented as a plug‐in of an ontology editor to enhance its ability of managing and reasoning in (large) ontologies.

In this paper, we investigate belief revision in possibilistic logic, which is a weighted logic proposed to deal with incomplete and uncertain information. Existing revision operators in possibilistic logic are restricted in the sense that the input information can only be a formula instead of a possibilistic knowledge base which is a set of weighted formulas. To break this restriction, we consider weighted prime implicants of a possibilistic knowledge base and use them to define novel revision operators in possibilistic logic. Intuitively, a weighted prime implicant of a possibilistic knowledge base is a logically weakest possibilistic term (i.e., a set of weighted literals) that can entail the knowledge base. We first show that the existing definition of a weighted prime implicant is problematic and need a modification. To define a revision operator using weighted prime implicants, we face two problems. The first problem is that we need to define the notion of a conflict set between two weighted prime implicants of two possibilistic knowledge bases to achieve minimal change. The second problem is that we need to define the disjunction of possibilistic terms. We solve these problems and define two conflict-based revision operators in possibilistic logic. We then adapt the well-known postulates for revision proposed by Katsuno and Mendelzon and show that our revision operators satisfy four of the basic adapted postulates and satisfy two others in some special cases.

The FLP semantics presented by (Faber, Leone, and Pfeifer 2004) has been widely used to define answer sets, called FLP answer sets, for different types of logic programs such as logic programs with aggregates, description logic programs (dl-programs), Hex programs, and logic programs with first-order formulas (general logic programs). However, it was recently observed that the FLP semantics may produce unintuitive answer sets with circular justifications caused by self-supporting loops. In this paper, we address the circular justification problem for general logic programs by enhancing the FLP semantics with a level mapping formalism. In particular, we extend the Gelfond-Lifschitz three step definition of the standard answer set semantics from normal logic programs to general logic programs and define for general logic programs the first FLP semantics that is free of circular justifications. We call this FLP semantics the well-justified FLP semantics. This method naturally extends to general logic programs with additional constraints like aggregates, thus providing a unifying framework for defining the well-justified FLP semantics for various types of logic programs. When this method is applied to normal logic programs with aggregates, the well-justified FLP semantics agrees with the conditional satisfaction based semantics defined by (Son, Pontelli, and Tu 2007); and when applied to dl-programs, the semantics agrees with the strongly well-supported semantics defined by (Shen 2011).

Revising knowledge bases (KBs) in description logics (DLs) in a syntax-independent manner is an important, nontrivial problem for the ontology management and DL communities. Several attempts have been made to adapt classical model-based belief revision and update techniques to DLs, but they are restricted in several ways. In particular, they do not provide operators or algorithms for general DL KB revision. The key difficulty is that, unlike propositional logic, a DL KB may have infinitely many models with complex (and possibly infinite) structures, making it difficult to define and compute revisions in terms of models. In this paper, we study general KBs in a specific DL in the DL-Lite family. We introduce the concept of features for such KBs, develop an alternative semantic characterization of KBs using features (instead of models), define two specific revision operators for KBs, and present the first algorithm for computing best approximations for syntax-independent revisions of KBs.

The language of HEX-programs under the answer-set semantics is designed for interoperating with heterogeneous sources via external atoms and for meta-reasoning via higher-order literals in the context of the semantic Web. As an important technique in managing knowledge bases, the notion of forgetting has received increasing interest in the knowledge-representation area. In this paper, we introduce a semantics-based theory of forgetting for HEX-programs and, in turn, for a class of OWL/RDF(S) ontologies which allows to fully employ semantic information in managing ontologies like editing, merging, aligning, and redundancy removal

Much work has been done on extending the well-founded semantics to general disjunctive logic programs and various approaches have been proposed. However, these semantics are different from each other and no consensus is reached about which semantics is the most intended. In this article, we look at disjunctive well-founded reasoning from different angles. We show that there is an intuitive form of the well-founded reasoning in disjunctive logic programming which can be characterized by slightly modifying some existing approaches to defining disjunctive well-founded semantics, including program transformations, argumentation, unfounded sets (and resolution-like procedure). By employing the techniques developed by Brass and Dix in their transformation-based approach, we also provide a bottom-up procedure for this semantics. The significance of our work is not only in clarifying the relationship among different approaches, but also shed some light on what is an intended well-founded semantics for disjunctive logic programs.

In recent years, there has been a large amount of disparate work concerning the representation and reasoning with qualitative preferential information by means of approaches to nonmonotonic reasoning. Given the variety of underlying systems, assumptions, motivations, and intuitions, it is difficult to compare or relate one approach with another. Here, we present an overview and classification for approaches to dealing with preference. A set of criteria for classifying approaches is given, followed by a set of desiderata that an approach might be expected to satisfy. A comprehensive set of approaches is subsequently given and classified with respect to these sets of underlying principles.

We provide a semantic framework for preference handling in answer set programming. To this end, we introduce preference preserving consequence operators. The resulting fixpoint characterizations provide us with a uniform semantic framework for characterizing preference handling in existing approaches. Although our approach is extensible to other semantics by means of an alternating fixpoint theory, we focus here on the elaboration of preferences under answer set semantics. Alternatively, we show how these approaches can be characterized by the concept of order preservation. These uniform semantic characterizations provide us with new insights about inter-relationships and moreover about ways of implementation.