Description Logic Knowledge Bases Research Articles

Approximate Reasoning for Large-Scale ABox in OWL DL Based on Neural-Symbolic Learning

The ontology knowledge base (KB) can be divided into two parts: TBox and ABox, where the former models schema-level knowledge within the domain, and the latter is a set of statements of assertions or facts about instances. ABox reasoning is a process of discovering implicit knowledge in ABox based on the existing KB, which is of great value in KB applications. ABox reasoning is influenced by both the complexity of TBox and scale of ABox. The traditional logic-based ontology reasoning methods are usually designed to be provably sound and complete but suffer from long algorithm runtimes and do not scale well for ontology KB represented by OWL DL (Description Logic). In some application scenarios, the soundness and completeness of reasoning results are not the key constraints, and it is acceptable to sacrifice them in exchange for the improvement of reasoning efficiency to some extent. Based on this view, an approximate reasoning method for large-scale ABox in OWL DL KBs was proposed, which is named the ChunfyReasoner (CFR). The CFR introduces neural-symbolic learning into ABox reasoning and integrates the advantages of symbolic systems and neural networks (NNs). By training the NN model, the CFR approximately compiles the logic deduction process of ontology reasoning, which can greatly improve the reasoning speed while ensuring higher reasoning quality. In this paper, we state the basic idea, framework, and construction process of the CFR in detail, and we conduct experiments on two open-source ontologies built on OWL DL. The experimental results verify the effectiveness of our method and show that the CFR can support the applications of large-scale ABox reasoning of OWL DL KBs.

Using Adaptive Logics for Expression of Context and Interoperability in DL Ontologies

Ontologies are logical theories that are used in computer science for describing different items such as web services, agents in multi-agent systems, or domain knowledge. Many ontologies exist, expressing various domains of knowledge with different abstraction levels (domain ontologies, top-level ontologies, and task ontologies are the usual categories). The conceptualization of the knowledge contained in an ontology is subject to change, whether because the context of its use changes, because the domain evolves, or because an ontology needs to interoperate with other elements using other ontologies. Change in logical theories is a form of defeasible reasoning, in which some formulas need to be added or removed from a knowledge base. Adaptive Logics (AL) is a logic managing defeasible reasoning that we investigate in this paper for managing change in ontologies expressed with Description Logics (DL). The adaptation of AL for DL will help express the context in which formulas remain valid or can be added to a DL knowledge base, and ease the interoperability between ontologies.

A commonsense reasoning framework for explanatory emotion attribution, generation and re-classification

We present DEGARI (Dynamic Emotion Generator And ReclassIfier), an explainable system for emotion attribution and recommendation. This system relies on a recently introduced commonsense reasoning framework, the TCL logic, which is based on a human-like procedure for the automatic generation of novel concepts in a Description Logics knowledge base. Starting from an ontological formalization of emotions based on the Plutchik model, known as ArsEmotica, the system exploits the logic TCL to automatically generate novel commonsense semantic representations of compound emotions (e.g. Love as derived from the combination of Joy and Trust according to Plutchik). The generated emotions correspond to prototypes, i.e. commonsense representations of given concepts, and have been used to reclassify emotion-related contents in a variety of artistic domains, ranging from art datasets to the editorial contents available in RaiPlay, the online platform of RAI Radiotelevisione Italiana (the Italian public broadcasting company). We show how the reported results (evaluated in the light of the obtained reclassifications, the user ratings assigned to such reclassifications, and their explainability) are encouraging, and pave the way to many further research directions.

Verification of fuzzy UML models with fuzzy Description Logic

The fuzzy UML model has been introduced to enable the conceptual modeling of imprecise data in many applications. How to prevent, detect, and correct errors as early as possible in the modeling process by verifying the correctness of fuzzy UML models is desirable. But it is difficult to manually verify the correctness of the models. Thanks to the effective reasoning service of fuzzy Description Logics (DLs), they are considered as natural candidates for supporting the verification of fuzzy UML models. In this paper we propose a complete and practical approach for verifying fuzzy UML models with fuzzy DLs. In detail, we first propose an approach for transforming a fuzzy UML model into a fuzzy DL knowledge base. Then we further reduce the verification tasks of the fuzzy UML model to reasoning problems of the transformed fuzzy DL knowledge base. Also, the correctness of the approach is proved, and a running example is provided to explain the approach in detail. Final we implemented a prototype that can transform fuzzy UML models into fuzzy DL knowledge bases. Case studies show that the proposed approach is feasible and the prototype translator actually works. By means of our approach and tool, the transformed fuzzy DL knowledge base and reasoning tasks can be input into the existing fuzzy DL reasoners, and the reasoning results reported by the reasoners can be passed back to the designer to improve the quality of the fuzzy UML model.

Minimally inconsistent reasoning in Semantic Web.

Reasoning with inconsistencies is an important issue for Semantic Web as imperfect information is unavoidable in real applications. For this, different paraconsistent approaches, due to their capacity to draw as nontrivial conclusions by tolerating inconsistencies, have been proposed to reason with inconsistent description logic knowledge bases. However, existing paraconsistent approaches are often criticized for being too skeptical. To this end, this paper presents a non-monotonic paraconsistent version of description logic reasoning, called minimally inconsistent reasoning, where inconsistencies tolerated in the reasoning are minimized so that more reasonable conclusions can be inferred. Some desirable properties are studied, which shows that the new semantics inherits advantages of both non-monotonic reasoning and paraconsistent reasoning. A complete and sound tableau-based algorithm, called multi-valued tableaux, is developed to capture the minimally inconsistent reasoning. In fact, the tableaux algorithm is designed, as a framework for multi-valued DL, to allow for different underlying paraconsistent semantics, with the mere difference in the clash conditions. Finally, the complexity of minimally inconsistent description logic reasoning is shown on the same level as the (classical) description logic reasoning.

DL-lite contraction and revision

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 op...

Axiomatisation of general concept inclusions from finite interpretations

Description logic knowledge bases can be used to represent knowledge about a particular domain in a formal and unambiguous manner. Their practical relevance has been shown in many research areas, especially in biology and the Semantic Web. However, the tasks of constructing knowledge bases itself, often performed by human experts, is difficult, time-consuming and expensive. In particular the synthesis of terminological knowledge is a challenge that every expert has to face. Because human experts cannot be omitted completely from the construction of knowledge bases, it would therefore be desirable to at least get some support from machines during this process. To this end, we shall investigate in this work an approach which shall allow us to extract terminological knowledge in the form of general concept inclusions from factual data, where the data is given in the form of vertex- and edge-labelled graphs. Because such graphs appear naturally within the scope of the Semantic Web in the form of sets of Resource Description Framework (RDF) triples, the presented approach opens up another possibility to extract terminological knowledge from the Linked Open Data Cloud.

Learning in Description Logics with Fuzzy Concrete Domains

Description Logics (DLs) are a family of logic-based Knowledge Representation (KR) formalisms, which are particularly suitable for representing incomplete yet precise structured knowl- edge. Several fuzzy extensions of DLs have been proposed in the KR field in order to handle im- precise knowledge which is particularly pervading in those domains where entities could be better described in natural language. Among the many approaches to fuzzification in DLs, a simple yet interesting one involves the use of fuzzy concrete domains. In this paper, we present a method for learning within the KR framework of fuzzy DLs. The method induces fuzzy DL inclusion axioms from any crisp DL knowledge base. Notably, the induced axioms may contain fuzzy concepts au- tomatically generated from numerical concrete domains during the learning process. We discuss the results obtained on a popular learning problem in comparison with state-of-the-art DL learning algorithms, and on a test bed in order to evaluate the classification performance.

DL-Lite Ontology Revision Based on An Alternative Semantic Characterization

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.

XPath for DL Ontologies

Applications of description logics (DLs) such as ontology-based data access (OBDA) require understanding of how to pose database queries over DL knowledge bases. While there have been many studies regarding traditional relational query formalisms such as conjunctive queries and their extensions, little attention has been paid to graph database queries, despite the fact that graph databases have essentially the same structure as knowledge bases. In particular, not much is known about the interplay between DLs and XPath. The latter is a powerful formalism for querying semistructured data: it is in the core of most practical query languages for XML trees, and it is also gaining popularity in theory and practice of graph databases. In this paper we make a step towards coupling knowledge bases and graph databases by studying how to answer powerful XPath-style queries over simple DLs like DL-Lite and EL. We start with adapting the definition of XPath to the DL context, and then proceed to study the complexity of evaluating XPath queries over knowledge bases. Results show that, while query answering is undecidable for the full XPath, by carefully tuning the shape of negation allowed in the queries we can arrive at XPath fragments that have a potential to be used in practice.

Similarity-based relaxed instance queries

In Description Logics (DL) knowledge bases (KBs), information is typically captured by clear-cut concepts. For many practical applications querying the KB by crisp concepts is too restrictive; a user might be willing to lose some precision in the query, in exchange of a larger selection of answers. Similarity measures can offer a controlled way of gradually relaxing a query concept within a user-specified limit.In this paper we formalize the task of instance query answering for DL KBs using concepts relaxed by concept similarity measures (CSMs). We investigate computation algorithms for this task in the DL EL, their complexity and properties for the CSMs employed regarding whether unfoldable or general TBoxes are used. For the case of general TBoxes we define a family of CSMs that take the full TBox information into account, when assessing the similarity of concepts.

The Complexity of Answering Conjunctive and Navigational Queries over OWL 2 EL Knowledge Bases

OWL 2 EL is a popular ontology language that supports role inclusions---that is, axioms that capture compositional properties of roles. Role inclusions closely correspond to context-free grammars, which was used to show that answering conjunctive queries (CQs) over OWL 2 EL knowledge bases with unrestricted role inclusions is undecidable. However, OWL 2 EL inherits from OWL 2 DL the syntactic regularity restriction on role inclusions, which ensures that role chains implying a particular role can be described using a finite automaton (FA). This is sufficient to ensure decidability of CQ answering; however, the FAs can be worst-case exponential in size so the known approaches do not provide a tight upper complexity bound. In this paper, we solve this open problem and show that answering CQs over OWL 2 EL knowledge bases is PSPACE-complete in combined complexity (i.e., the complexity measured in the total size of the input). To this end, we use a novel encoding of regular role inclusions using bounded-stack pushdown automata---that is, FAs extended with a stack of bounded size. Apart from theoretical interest, our encoding can be used in practical tableau algorithms to avoid the exponential blowup due to role inclusions. In addition, we sharpen the lower complexity bound and show that the problem is PSPACE-hard even if we consider only role inclusions as part of the input (i.e., the query and all other parts of the knowledge base are fixed). Finally, we turn our attention to navigational queries over OWL 2 EL knowledge bases, and we show that answering positive, converse-free conjunctive graph XPath queries is PSPACE-complete as well; this is interesting since allowing the converse operator in queries is known to make the problem EXPTIME-hard. Thus, in this paper we present several important contributions to the landscape of the complexity of answering expressive queries over description logic knowledge bases.

On bisimulations for description logics

We study bisimulations for useful description logics. The simplest among the considered logics is ALCreg (a variant of PDL). The others extend that logic with the features: inverse roles, nominals, qualified number restrictions, the universal role, and/or the concept constructor for expressing the local reflexivity of a role. They also allow role axioms. Our contributions are as follows. We propose to treat named individuals as initial states and give an appropriate bisimulation condition for that. We also give bisimulation conditions for the universal role and the concept constructor ∃r.Self. We prove that all of the bisimulation conditions for the features can be combined together to guarantee invariance of concepts and the Hennessy-Milner property for the whole class of studied description logics. We address and give results on invariance or preservation of ABoxes, RBoxes and knowledge bases in description logics. Independently from Lutz et al. [26,27] we also give results on invariance of TBoxes. We introduce a new notion called QS-interpretation, which is needed for dealing with minimizing interpretations in description logics with qualified number restrictions and/or the concept constructor ∃r.Self. We formulate and prove results on minimality of quotient interpretations w.r.t. the largest auto-bisimulations. We adapt Hopcroft’s automaton minimization algorithm to give an efficient algorithm for computing the partition corresponding to the largest auto-bisimulation of a finite interpretation in any description logic of the considered family. Using the invariance results we compare the expressiveness of the considered description logics w.r.t. concepts, TBoxes and ABoxes. Our results about separating the expressiveness of description logics are naturally extended to the case when instead of ALCreg we have any sublogic of ALCreg that extends ALC.

Goal-oriented modeling and verification of feature-oriented product lines

Goal models represent requirements and intentions of a software system. They play an important role in the development life cycle of software product lines (SPLs). In the domain engineering phase, goal models guide the development of variability in SPLs by providing the rationale for the variability, while they are used for the configuration of SPLs in the application engineering phase. However, variability in SPLs, which is represented by feature models, usually has design and implementation-induced constraints. When those constraints are not aligned with variability in goal models, the configuration with goal models becomes error prone. To remedy this problem, we propose a description logic (DL)-based approach to represent both models and their relations in a common DL knowledge base. Moreover, we apply reasoning to detect inconsistencies in the variability of goal and feature models. A formal proof is provided to demonstrate the correctness of the reasoning approach. An empirical evaluation shows computational tractability of the inconsistency detection.

Inconsistency-tolerant reasoning with OWL DL

The Web Ontology Language (OWL) is a family of description logic based ontology languages for the Semantic Web and gives well defined meaning to web accessible information and services. The study of inconsistency-tolerant reasoning with description logic knowledge bases is especially important for the Semantic Web since knowledge is not always perfect within it. An important challenge is strengthening the inference power of inconsistency-tolerant reasoning because it is normally impossible for paraconsistent logics to obey all important properties of inference together. This paper presents a non-classical DL called quasi-classical description logic (QCDL) to tolerate inconsistency in OWL DL which is a most important sublanguage of OWL supporting those users who want the maximum expressiveness while retaining computational completeness (i.e., all conclusions are guaranteed to be computable) and decidability (i.e., all computations terminate in finite time). Instead of blocking those inference rules, we validate them conditionally and partially, under which more useful information can still be inferred when inconsistency occurs. This new non-classical DL possesses several important properties as well as its paraconsistency in DL, but it does not bring any extra complexity in worst case. Finally, a transformation-based algorithm is proposed to reduce reasoning problems in QCDL to those in DL so that existing OWL DL reasoners can be used to implement inconsistency-tolerant reasoning. Based on this algorithm, a prototype OWL DL paraconsistent reasoner called PROSE is implemented. Preliminary experiments show that PROSE produces more intuitive results for inconsistent knowledge bases than other systems in general.

Description Logic Knowledge and Action Bases

Description logic Knowledge and Action Bases (KAB) are a mechanism for providing both a semantically rich representation of the information on the domain of interest in terms of a description logic knowledge base and actions to change such information over time, possibly introducing new objects. We resort to a variant of DL-Lite where the unique name assumption is not enforced and where equality between objects may be asserted and inferred. Actions are specified as sets of conditional effects, where conditions are based on epistemic queries over the knowledge base (TBox and ABox), and effects are expressed in terms of new ABoxes. In this setting, we address verification of temporal properties expressed in a variant of first-order mu-calculus with quantification across states. Notably, we show decidability of verification, under a suitable restriction inspired by the notion of weak acyclicity in data exchange.

Description logic knowledge and action bases

Description logic Knowledge and Action Bases (KAB) are a mechanism for providing both a semantically rich representation of the information on the domain of interest in terms of a description logic...

Weight-based consistent query answering over inconsistent $${\mathcal {SHIQ}}$$ knowledge bases

Non-standard query mechanisms that work under inconsistency are required in some important description logic (DL)-based applications, including those involving an inconsistent DL knowledge base ( KB) whose intensional knowledge is consistent but is violated by its extensional knowledge. This paper proposes a weight-based semantics for querying such an inconsistent KB. This semantics defines an answer of a conjunctive query posed upon an inconsistent KB as a tuple of individuals whose substitution for the variables in the query head makes the query body entailed by any subbase of the KB consisting of the intensional knowledge and a weight-maximally consistent subset of the extensional knowledge. A novel computational method for this semantics is proposed, which works for extensionally reduced\({\mathcal {SHIQ}}\) KBs and conjunctive queries without non-distinguished variables. The method first compiles the given KB to a propositional program; then, for any given conjunctive query, it reduces the problem of computing all answers of the given query to a set of propositional satisfiability (SAT) problems with PB-constraints, which are then solved by SAT solvers. A decomposition-based framework for optimizing the method is also proposed. The feasibility of this method is demonstrated in our experiments.

Knowledge-Based Description Logic ALCO Knowledge Compiled Algorithm to Determine Consistency

Knowledge compilation is a common technique for propositional logic knowledge bases. A given knowledge base is transformed into a normal form, for which reasoning can be answered efficiently. The precompilation of description logic knowledge base is important for reasoning and services of description logic. This paper gives precompilation about the description logic ALCO TBox based on knowledge compilation techniques, for which the consistency of TBox can be determined.

Query Answering with DBoxes is Hard

Data in description logic knowledge bases is stored in the form of an ABox. ABoxes are often confusing for developers coming from relational databases because an ABox, in contrast to a database instance, provides an incomplete specification. A recently introduced assertional component of a description logic knowledge base is a DBox, which behaves more like a database instance. In this paper, we study the data complexity of query answering in the description logic DL-LiteF extended with DBoxes. DL-LiteF is a description logic tailored for data intensive applications and the data complexity of query answering in DL-LiteF with ABoxes is tractable (in AC0). Our main result is that this problem becomes coNP-complete with DBoxes. In some expressive description logics, query answering with DBoxes also leads to a higher (combined) complexity than query answering with ABoxes. As a proof of concept, we relate query answering in ALCFIO, i.e., ALC with Functional and Inverse roles, and nOminals to the same problem in ALCFI with DBoxes. The exact complexity of the former is an open problem in the description logic literature. Here we show that query answering in ALCFIO and ALCFI with DBoxes are mutually reducible to each other in polynomial time.All the proofs in this paper are available in the appendix for the reviewersʼ convenience.