Description Logic Ontologies Research Articles

Controlled query evaluation in description logics through consistent query answering

Controlled Query Evaluation (CQE) is a framework for the protection of confidential data, where a policy given in terms of logic formulae indicates which information must be kept private. Functions called censors filter query answering so that no answers are returned that may lead a user to infer data protected by the policy. The preferred censors, called optimal censors, are the ones that conceal only what is necessary, thus maximizing the returned answers. Typically, given a policy over a data or knowledge base, several optimal censors exist.Our research on CQE is based on the following intuition: confidential data are those that violate the logical assertions specifying the policy, and thus censoring them in query answering is similar to processing queries in the presence of inconsistent data as studied in Consistent Query Answering (CQA). In this paper, we investigate the relationship between CQE and CQA in the context of Description Logic ontologies. We borrow the idea from CQA that query answering is a form of skeptical reasoning that takes into account all possible optimal censors. This approach leads to a revised notion of CQE, which allows us to avoid making an arbitrary choice on the censor to be selected, as done by previous research on the topic.We then study the data complexity of query answering in our CQE framework, for conjunctive queries issued over ontologies specified in the popular Description Logics DL-LiteR and EL⊥. In our analysis, we consider some variants of the censor language, which is the language used by the censor to enforce the policy. Whereas the problem is in general intractable for simple censor languages, we show that for DL-LiteR ontologies it is first-order rewritable, and thus in AC0 in data complexity, for the most expressive censor language we propose.

A Gentle Introduction to Controlled Query Evaluation in DL-Lite Ontologies

Controlled query evaluation (CQE) is an approach for confidentiality-preserving query answering where a function called censor alters query answers so that users can never infer data that are protected by a policy given in terms of logic formulae. In this paper, we review some foundational results we have recently found in the context of CQE over Description Logic ontologies. In more detail, we discuss the main characteristics of two notions of censor, CQ censor and GA censor, focusing on the computational complexity of query answering and on the notion of indistinguishability. The latter is a desirable property imposing that a censor always makes a user believe that the underlying data instance might not contain confidential data. As for computational aspects, we characterize the data complexity of answering conjunctive queries for the relevant and practical case of DL-LiteR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {DL-Lite} _{{\\mathcal {R}}}$$\\end{document} ontologies. Since neither CQ censors nor GA censors enjoy both indistinguishability and tractability of query answering in the analyzed setting, we finally recall the notion of IGA censors, a sound approximation of GA censors which instead enjoys both properties, thus paving the way for robust and practical CQE for DL-LiteR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {DL-Lite} _{{\\mathcal {R}}}$$\\end{document} ontologies.

SMT Safety Verification of Ontology-Based Processes

In the context of verification of data-aware processes, a formal approach based on satisfiability modulo theories (SMT) has been considered to verify parameterised safety properties. This approach requires a combination of model-theoretic notions and algorithmic techniques based on backward reachability. We introduce here Ontology-Based Processes, which are a variant of one of the most investigated models in this spectrum, namely simple artifact systems (SASs), where, instead of managing a database, we operate over a description logic (DL) ontology. We prove that when the DL is expressed in (a slight extension of) RDFS, it enjoys suitable model-theoretic properties, and that by relying on such DL we can define Ontology-Based Processes to which backward reachability can still be applied. Relying on these results we are able to show that in this novel setting, verification of safety properties is decidable in PSPACE.

Consequence-based Axiom Pinpointing for Expressive Description Logic Ontologies

Consequence-based Axiom Pinpointing for Expressive Description Logic Ontologies

Description Logic Ontology-Supported Part Orientation for Fused Deposition Modelling

Fused deposition modelling (FDM) is well-known as an inexpensive and the most commonly used additive manufacturing process. In FDM, build orientation is one of the critical factors that affect the quality of the printed part. However, the activity of determining a build orientation for an FDM part, i.e., part orientation for FDM, usually relies on the knowledge and experience of domain experts. This necessitates an approach that enables the capture, representation, reasoning, and reuse of the data and knowledge in this activity. In this paper, a description logic (DL) ontology-supported part orientation approach for FDM is presented. Firstly, a set of top-level entities are created to construct a DL ontology for FDM part orientation. Then a DL ontology-supported alternative orientation generation procedure, a DL ontology-supported factor value prediction procedure, and a DL ontology-supported optimal orientation selection procedure are developed successively. After that, the application of the presented approach is illustrated via part orientation on six FDM parts. Finally, the effectiveness and efficiency of the presented approach are demonstrated through theoretical predictions and printing experiments and the advantages of the approach are demonstrated via an example. The demonstration results suggest that the presented approach has satisfying effectiveness and efficiency and provides a semantic enrichment model for capturing and representing FDM part orientation data and knowledge to enable automatic checking, reasoning, query, and further reuse.

Expressivity of Planning with Horn Description Logic Ontologies

State constraints in AI Planning globally restrict the legal environment states. Standard planning languages make closed-domain and closed-world assumptions. Here we address open-world state constraints formalized by planning over a description logic (DL) ontology. Previously, this combination of DL and planning has been investigated for the light-weight DL DL-Lite. Here we propose a novel compilation scheme into standard PDDL with derived predicates, which applies to more expressive DLs and is based on the rewritability of DL queries into Datalog with stratified negation. We also provide a new rewritability result for the DL Horn-ALCHOIQ, which allows us to apply our compilation scheme to quite expressive ontologies. In contrast, we show that in the slight extension Horn-SROIQ no such compilation is possible unless the weak exponential hierarchy collapses. Finally, we show that our approach can outperform previous work on existing benchmarks for planning with DL ontologies, and is feasible on new benchmarks taking advantage of more expressive ontologies.

Modeling Abstract Algebra as an OWL Ontology (Student Abstract)

Description logic ontologies serve to model classifications and structural relationships, and to represent and reason about domain knowledge. Modeling the basic classification of abstract algebraic structures as an ontology demonstrates the difficulties presented by their logical semantics, and shed light on the limitations to accurately model further topics in algebra and related mathematical domains.

A tetrachotomy of ontology-mediated queries with a covering axiom

Our concern is the problem of efficiently determining the data complexity of answering queries mediated by description logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology-based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple covering axiom stating that one class is covered by the union of two other classes. We show that, on the one hand, these rudimentary ontology-mediated queries, called disjunctive sirups (or d-sirups), capture many features and difficulties of the general case. For example, answering d-sirups is Π2p-complete for combined complexity and can be in ▪ or L-, NL-, P-, or coNP-complete for data complexity (with the problem of recognising FO-rewritability of d-sirups being 2ExpTime-hard); some d-sirups only have exponential-size resolution proofs, some only double-exponential-size positive existential FO-rewritings and single-exponential-size nonrecursive datalog rewritings. On the other hand, we prove a few partial sufficient and necessary conditions of FO- and (symmetric/linear-) datalog rewritability of d-sirups. Our main technical result is a complete and transparent syntactic ▪/NL/P/coNP tetrachotomy of d-sirups with disjoint covering classes and a path-shaped Boolean conjunctive query. To obtain this tetrachotomy, we develop new techniques for establishing P- and coNP-hardness of answering non-Horn ontology-mediated queries as well as showing that they can be answered in NL.

Forgetting and Consequence-Based Knowledge Extraction for Description Logic Ontologies

Forgetting and Consequence-Based Knowledge Extraction for Description Logic Ontologies

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.

Answering Fuzzy Queries over Fuzzy DL-Lite Ontologies

AbstractA prominent problem in knowledge representation is how to answer queries taking into account also the implicit consequences of an ontology representing domain knowledge. While this problem has been widely studied within the realm of description logic ontologies, it has been surprisingly neglected within the context of vague or imprecise knowledge, particularly from the point of view of mathematical fuzzy logic. In this paper, we study the problem of answering conjunctive queries and threshold queries w.r.t. ontologies in fuzzy DL-Lite. Specifically, we show through a rewriting approach that threshold query answering w.r.t. consistent ontologies remains in ${AC}^{0}$ in data complexity, but that conjunctive query answering is highly dependent on the selected triangular norm, which has an impact on the underlying semantics. For the idempotent Gödel t-norm, we provide an effective method based on a reduction to the classical case.

Query Rewriting for Horn-SHIQ Plus Rules

Query answering over Description Logic (DL) ontologies has become a vibrant field of research. Efficient realizations often exploit database technology and rewrite a given query to an equivalent SQL or Datalog query over a database associated with the ontology. This approach has been intensively studied for conjunctive query answering in the DL-Lite and EL families, but is much less explored for more expressive DLs and queries. We present a rewriting-based algorithm for conjunctive query answering over Horn-SHIQ ontologies, possibly extended with recursive rules under limited recursion as in DL+log. This setting not only subsumes both DL-Lite and EL, but also yields an algorithm for answering (limited) recursive queries over Horn-SHIQ ontologies (an undecidable problem for full recursive queries). A prototype implementation shows its potential for applications, as experiments exhibit efficient query answering over full Horn-SHIQ ontologies and benign downscaling to DL-Lite, where it is competitive with comparable state of the art systems.

Enhancing Probabilistic Model Checking with Ontologies

Probabilistic model checking (PMC) is a well-established method for the quantitative analysis of state based operational models such as Markov decision processes. Description logics (DLs) provide a well-suited formalism to describe and reason about knowledge and are used as basis for the web ontology language (OWL). We investigate how such knowledge described by DLs can be integrated into the PMC process, introducing ontology-mediated PMC. Specifically, we propose ontologized programs as a formalism that links ontologies to behaviors specified by probabilistic guarded commands, the de-facto standard input formalism for PMC tools such as Prism. Through DL reasoning, inconsistent states in the modeled system can be detected. We present three ways to resolve these inconsistencies, leading to different Markov decision process semantics. We analyze the computational complexity of checking whether an ontologized program is consistent under these semantics. Further, we present and implement a technique for the quantitative analysis of ontologized programs relying on standard DL reasoning and PMC tools. This way, we enable the application of PMC techniques to analyze knowledge-intensive systems.We evaluate our approach and implementation on amulti-server systemcase study,where different DL ontologies are used to provide specifications of different server platforms and situations the system is executed in.

On Approximation of Concept Similarity Measure in Description Logic ELH With Pre-Trained Word Embedding

Data-driven and knowledge-driven methods are two mainstream techniques in the pursuit of developing artificial intelligence systems. While data-driven methods seek to develop a decision model from observations in the real world, they are difficult to provide an explanation for the results in human terms. On the other hand, knowledge-driven methods that employ symbolic reasoning based on formal semantics of a knowledge-base are thus more interpretable and explainable, while lacking an ability to deal with incomplete modeling of the structured knowledge-bases. This work aims to tackle these issues on ontology similarity by proposing a general framework that combines the strengths of both approaches for measuring semantic similarity of concepts in a description logic (DL) ontology. More specifically, a neuro-symbolic integrated framework is defined to exploit the pre-trained word embeddings with semantic definitions in an ontology to yield an explainable degree of concept similarity. To demonstrate its applicability, we develop a concrete similarity measure $ {\textsf {sim}}_\epsilon $ conforming to the proposed framework and also introduce an efficient algorithm that can extract an explanation for why such a degree is indicated. The correctness is shown by analyzing theoretical properties that it guarantees to preserve and also by performing an empirical evaluation with a medical ontology SNOMED CT and a medical pre-trained embedding BioWordVec. The results show that our proposed method remains both interpretability and explainability while achieving comparable performance, relative to the state-of-the-art approaches in the data and knowledge-driven methods.

An SQL Domain Ontology Learning for Analyzing Hierarchies of Structures in Pre-Learning Assessment Agents

This paper presents the use of description logics (DL) in the definition and development of a Structured Query Language (SQL) domain ontology for a multi-agent based pre-assessment system. Description logics is a knowledge representation language for defining terms or classes, the relationships between classes, their instances, including individuals and literals. In a formal school curriculum, modules of learning are inter-dependent. So, teaching and learning follows an ordered sequence of learning from lower-level module(s) to higher-level ones. This process enables students to gain mastery of lower-level materials before moving up the ladder to higher-level learning. To describe an SQL ontology and its representation for a multi-agent based system application, this paper uses a description logic language to present the organization of learning modules into DesiredConcept $$ $$ , PrerequisiteConcept $$ $$ and LeafNodes $$ $$ as well as their associated relationships, namely, hasPrerequisite and hasKB between the learning modules. The paper thus presents a TBox and an Abox of a DL ontology and further transformation into a first-order predicate for a multi-agent based system that was implemented in Jason.

Constructing and Extending Description Logic Ontologies using Methods of Formal Concept Analysis

My thesis describes how methods from Formal Concept Analysis can be used for constructing and extending description logic ontologies. In particular, it is shown how concept inclusions can be axiomatized from data in the description logics mathcal {E}mathcal {L}, mathcal {M}, textsf {Horn}-mathcal {M}, and textsf{Prob}text{-}mathcal {E}mathcal {L}. All proposed methods are not only sound but also complete, i.e., the result not only consists of valid concept inclusions but also entails each valid concept inclusion. Moreover, a lattice-theoretic view on the description logic mathcal {E}mathcal {L} is provided. For instance, it is shown how upper and lower neighbors of mathcal {E}mathcal {L} concept descriptions can be computed and further it is proven that the set of mathcal {E}mathcal {L} concept descriptions forms a graded lattice with a non-elementary rank function.

Reasoning in Description Logic Ontologies for Privacy Management

This work is initially motivated by a privacy scenario in which the confidential information about persons or its properties formulated in description logic (DL) ontologies should be kept hidden. We investigate procedures to detect whether this confidential information can be disclosed in a certain situation by using DL formalisms. If it is the case that this information can be deduced from the ontologies, which implies certain privacy policies are not fulfilled, then one needs to consider methods to repair these ontologies in a minimal way such that the modified ontologies complies with the policies. However, privacy compliance itself is not enough if a possible attacker can also obtain relevant information from other sources, which together with the modified ontologies might violate the privacy policy. This article provides a summary of studies and results from Adrian Nuradiansyah’s Ph.D. dissertation that are corresponding to the addressed problem above with a special emphasis on the investigations on the worst-case complexities of those problems as well as the complexity of the procedures and algorithms solving the problems.

Learning Description Logic Ontologies: Five Approaches. Where Do They Stand?

The quest for acquiring a formal representation of the knowledge of a domain of interest has attracted researchers with various backgrounds into a diverse field called ontology learning. We highlight classical machine learning and data mining approaches that have been proposed for (semi-)automating the creation of description logic (DL) ontologies. These are based on association rule mining, formal concept analysis, inductive logic programming, computational learning theory, and neural networks. We provide an overview of each approach and how it has been adapted for dealing with DL ontologies. Finally, we discuss the benefits and limitations of each of them for learning DL ontologies.

LETHE: Forgetting and Uniform Interpolation for Expressive Description Logics

Uniform interpolation and forgetting describe the task of projecting a given ontology into a user-specified vocabulary, that is, of computing a new ontology that only uses names from a specified set of names, while preserving all logical entailments that can be expressed with those names. This is useful for ontology analysis, ontology reuse and privacy. Lethe is a tool for performing uniform interpolation on ontologies in expressive description logics, and it can be used from the command line, using a graphical interface, and as a Java library. It furthermore implements methods for computing logical difference and performing abduction using uniform interpolation. We present the tool together with an evaluation on a varied corpus of realistic ontologies.

Resilient Logic Programs: Answer Set Programs Challenged by Ontologies

We introduce resilient logic programs (RLPs) that couple a non-monotonic logic program and a first-order (FO) theory or description logic (DL) ontology. Unlike previous hybrid languages, where the interaction between the program and the theory is limited to consistency or query entailment tests, in RLPs answer sets must be ‘resilient’ to the models of the theory, allowing non-output predicates of the program to respond differently to different models. RLPs can elegantly express ∃∀∃-QBFs, disjunctive ASP, and configuration problems under incompleteness of information. RLPs are decidable when a couple of natural assumptions are made: (i) satisfiability of FO theories in the presence of closed predicates is decidable, and (ii) rules are safe in the style of the well-known DL-safeness. We further show that a large fragment of such RLPs can be translated into standard (disjunctive) ASP, for which efficient implementations exist. For RLPs with theories expressed in DLs, we use a novel relaxation of safeness that safeguards rules via predicates whose extensions can be inferred to have a finite bound. We present several complexity results for the case where ontologies are written in some standard DLs.