DOCSLIB.ORG

Generating Ontologies from Templates: a Rule-Based Approach for Capturing Regularity

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Generating Ontologies from Templates: a Rule-Based Approach for Capturing Regularity Generating Ontologies from Templates: A Rule-Based Approach for Capturing Regularity Henrik Forssell Christian Kindermann Daniel P.Lupp Uli Sattler Evgenij Thorstensen Technical Report Contents 1 Introduction2 1.1 Examples . .3 2 Preliminaries7 3 Generators and GBoxes8 4 Results9 4.1 GBox containment and equivalence . 11 4.2 GBoxes with negation . 12 5 Related work 16 6 Future work 17 arXiv:1809.10436v1 [cs.AI] 27 Sep 2018 1 Abstract We present a second-order language that can be used to succinctly specify ontologies in a consistent and transparent manner. This language is based on ontology templates (OTTR), a framework for capturing recurring patterns of axioms in ontological modelling. The language, and our results are indepen- dent of any specific DL. We define the language and its semantics, including the case of negation-as- failure, investigate reasoning over ontologies specified using our language, and show results about the decidability of useful reasoning tasks about the language itself. We also state and discuss some open problems that we believe to be of interest. 1 Introduction The phenomenon of frequently occurring structures in ontologies engineering (OE) has received attention from a variety of angles. One of the first accounts is given in [6], where repeated versions of general conceptual models are identified. Similar observations gave rise to the notion of Ontology Design Patterns (ODP) as abstract descriptions of best practices in OE [15,4, 22 ]. Another view, emphasizing common ontological distinctions, led to the emergence of Upper Ontologies which aim to categorize general ideas shareable across different domains [16]. Orthogonal to such conceptual patterns, the existence of syntactic regularities in ontologies has been noted and some aspects of their nature have been analyzed [30, 29, 31]. In this paper, we propose a new language that allows expressing patterns of re- peated structures in ontologies. This language is rule-based and has both a model- theoretic and a fixpoint semantics, for which we show that they coincide. In con- trast to other rule languages “on top of” DLs, in this language, firing a rule results in the addition of TBox and/or ABox axioms, with the goal to succinctly describe ontologies, thereby making them more readable and maintainable. Given that DL ontologies are sets of axioms, an ontology provides no means to arrange its axioms in a convenient manner for ontology engineers. In particular, it is not possible to group conceptually related axioms or indicate interdependen- cies between axioms. While ontology editors such as Protégé1 display an ontology through a hierarchy of its entities, conceptual interdependencies between axioms are hidden and the underlying structural design of an ontology remains obfuscated. Example 1.1 Consider the ontology O1 = Jaguar Animal, Jaguar hasChild.Jaguar, (1) f Tiger v Animal, Tiger v 8hasChild.Tiger, (2) Lion v Animal, Lion v 8hasChild.Lion (3) v v 8 g Then, an ontology editor will group the entities Jaguar, Tiger and Lion under Animal according to their class hierarchy. However, O1 contains no indication that every subclass X of Animal can have only children of the same class X . Assume this regularity is no coincidence but a desired pattern that should hold for any subclass of Animal. Currently, ontol- ogy engineers have no means of expressing or enforcing such a pattern other than 1 https://protege.stanford.edu/ 2 dealing with the ontology as a whole, inspecting all axioms separately, and making necessary changes manually. Expressing patterns such as in Example 1.1 explicitly has a potential to reveal some aspects of the intentions for the design of an ontology. Example 1.2 Consider the ontology O Jaguar Animal, Tiger Animal, Lion Animal 2 = f v v v g In addition, consider the rule g : ?X Animal ?X hasChild.?X , f| v{z }g !| f v 8 {z }g Body Head where ?X is a variable. We can interpret the body of this rule as a query which, when evaluated over the ontology O2, returns substitutions for ?X . These substitutions can then be used to instantiate the axioms in the head of the rule. Firing the above rule over O2 would add all those resulting axioms to O2, thereby reconstructing O1 from Example 1.1. In the following, we will call such rules generators. The possible benefits of generators are threefold. Firstly, O2 in combination with g is easier to understand because g makes a statement about all subconcepts of Animal that the type of an animal determines the type of its children. This is a kind of meta-statement about concepts which a user of an ontology can usually only learn by inspecting (many) axioms in an ontology. Secondly, O2 in combination with g is easier to maintain and extend compared to O1, where a user would have to manually ensure that the meta-statement continues to be satisfied after new concepts have been added. Thirdly, conceptual relationships captured in a generator such as g are easy to reuse and can foster interoperability between ontologies in the spirit of ontology design patterns. We close this section with more elaborate examples to demonstrate the benefits generators such as g can provide. 1.1 Examples Example 1.3 (Composition) Assume we want to model typical roles in groups of social predatory animals. One such a role would be that of a hunter. A challenge for representing such knowledge is that different collective nouns are used for different animals, e.g. a group of lions is called a “pride”, a group of wild dogs is called a “pack”, a group of killer whales is called a “pod”, etc. Therefore, a mechanism that can conveniently iterate over all these group formations would be beneficial. Consider the following query Q1: 3 Q1 = ?X Animal, (4) f?X v eats.Animal, (5) ?X v 9hunts.Animal, (6) ?Y vSocialGroup 9 , (7) ?X v socialisesIn.?Y, (8) ?Y v 9hasMember.?X , (9) v 9 socialisesIn hasMember− (10) ≡ g Lines4–6 bind the variable ? X to a predatory animal. Line7 binds the variable ? Y to a type of social group and lines8–10 associate a particular type of animal with its respective social group. Given the bindings for ?X and ?Y it is straightforward to express that a particular type of predator ?X is a hunter in its respective social group, namely: ?Y hasHunter.?X . A generator such as in Example 1.2 could capture this relationship:v 9 g1 : Q1 ?Y hasHunter.?X ! f v 9 g Example 1.4 (Extension) Extending generator g1 from Example 1.3 to capture more specialised knowledge is straightforward. Consider predatory ants of the family Formicidae. These ants generally live in colonies with an elaborate social organisation consisting of workers, drones, queens, etc. First, we extend query Q1 with the following axioms: Q2 = Q1 ?X Formicidae, (11) [ f?Z v?Y (12) ?X v socialisesIn.?Z (13) v 9 g Axiom 11 requires ?X to bind to a type of Formicidae, e.g. ?X = SafariAnt. Ac- cording to query Q1, the variable ?Y binds to a general SocialGroup, e.g. ?Y = AntColony. Then, axiom 12 binds ?Z to a more specialised subgroup of a ?Y . Finally, axiom 13 ensures that this subgroup ?Z is associated with ?X . So for ?X = SafariAnt we get ?Z = SafariAntColony. Next, we can specify the generator to add all desired axioms based on matches of query Q2 specialised for ants: g2 : Q2 ?Z ! hasHunter.?X , f?Z v 9hasWorker.?X , ?Z v 9hasDrone.?X , ?Z v 9hasQueen.?X v 9 g Note how the body and head of generator g1 from Example 1.3 have been reused and extended only by set unions. Example 1.5 (Negative Guards) Often, general relationships are subject to excep- tions. While most ants hunt and feed cooperatively, there are some genera of ants, 4 e.g. Myrmecia, that do not. Therefore, g2 in Example 1.4 would generate an unde- sired axiom, namely MyrmeciaAntColony hasHunter.MyrmeciaAnt. This moti- vates guards in the body of generators that mayv not only specify positive constraints but also negative ones: Q3 = Q2 not ?X MyrmeciaAnt, [ fnot ?Z v MyrmeciaAntColony v g g3 : Q3 ?Z ! hasHunter.?X , f?Z v 9hasWorker.?X , ?Z v 9hasDrone.?X , ?Z v 9hasQueen.?X v 9 g One might argue that the effect of negative guards could also be achieved by positive guards using negated concepts in DL, i.e. ?X MyrmeciaAnt instead of not?X MyrmeciaAnt. However, this approach wouldv necessitate : the introduction of a potentiallyv large number of axioms of type ?X MyrmeciaAnt in the given ontology. This can be avoided by using g3. v : Another advantage of negative guards is the possibility to explicitly express de- fault assumptions for lack of better knowledge. An ant colony of a certain genus usually consists of only ants of this genus, e.g. SafariAntColony hasMember.SafariAnt. (14) v 8 However, some genera of ants are social parasites that enslave other ant species. In such a case, the default assumption about the homogeneity of an ant colony is wrong and the axiom 14 should not be added. Q4 = ?X Ant, f?Y v AntColony, ?Y v hasMember.?X , ?Z vAnt 9 , ?X v ?Z, not ?X v :enslaves.?Z, not ?Y v 9hasMember.?Z, v 9 g g : Q ?Y hasMember.?X 4 4 ! f v 8 g Example 1.6 (Recursion) Contagious diseases may be transmitted between ani- mals sharing a habitat. Overlapping habitats of infected animals may result in a propagation of diseases across habitats. Assume there is an overlap between habitats H1, H2, H3 such that there is no overlap between H1 and H3, H12 describes the overlap between H1 and H2, and H23 describes the overlap between H2 and H3 (see Figure1).
Load more

Recommended publications
  • A Logical Framework for Modularity of Ontologies∗
    A Logical Framework for Modularity of Ontologies∗ Bernardo Cuenca Grau, Ian Horrocks, Yevgeny Kazakov and Ulrike Sattler The University of Manchester School of Computer Science Manchester, M13 9PL, UK {bcg, horrocks, ykazakov, sattler }@cs.man.ac.uk Abstract ontology itself by possibly reusing the meaning of external symbols. Hence by merging an ontology with external on- Modularity is a key requirement for collaborative tologies we import the meaning of its external symbols to de- ontology engineering and for distributed ontology fine the meaning of its local symbols. reuse on the Web. Modern ontology languages, To make this idea work, we need to impose certain con- such as OWL, are logic-based, and thus a useful straints on the usage of the external signature: in particular, notion of modularity needs to take the semantics of merging ontologies should be “safe” in the sense that they ontologies and their implications into account. We do not produce unexpected results such as new inconsisten- propose a logic-based notion of modularity that al- cies or subsumptions between imported symbols. To achieve lows the modeler to specify the external signature this kind of safety, we use the notion of conservative exten- of their ontology, whose symbols are assumed to sions to define modularity of ontologies, and then prove that be defined in some other ontology. We define two a property of some ontologies, called locality, can be used restrictions on the usage of the external signature, to achieve modularity. More precisely, we define two no- a syntactic and a slightly less restrictive, seman- tions of locality for SHIQ TBoxes: (i) a tractable syntac- tic one, each of which is decidable and guarantees tic one which can be used to provide guidance in ontology a certain kind of “black-box” behavior, which en- editing tools, and (ii) a more general semantic one which can ables the controlled merging of ontologies.
    [Show full text]
  • Deciding Semantic Matching of Stateless Services∗
    Deciding Semantic Matching of Stateless Services∗ Duncan Hull†, Evgeny Zolin†, Andrey Bovykin‡, Ian Horrocks†, Ulrike Sattler†, and Robert Stevens† School of Computer Science, Department of Computer Science, † ‡ University of Manchester, UK University of Liverpool, UK Abstract specifying automated reasoning algorithms for such stateful service descriptions is basically impossible in the presence We present a novel approach to describe and reason about stateless information processing services. It can of any expressive ontology (Baader et al. 2005). Stateless- be seen as an extension of standard descriptions which ness implies that we do not need to formulate pre- and post- makes explicit the relationship between inputs and out- conditions since our services do not change the world. puts and takes into account OWL ontologies to fix the The question we are interested in here is how to help the meaning of the terms used in a service description. This biologist to find a service he or she is looking for, i.e., a allows us to define a notion of matching between ser- service that works with inputs and outputs the biologist can vices which yields high precision and recall for service provide/accept, and that provides the required functionality. location. We explain why matching is decidable, and The growing number of publicly available biomedical web provide biomedical example services to illustrate the utility of our approach. services, 3000 as of February 2006, required better match- ing techniques to locate services. Thus, we are concerned with the question of how to describe a service request Q Introduction and service advertisements Si such that the notion of a ser- Understanding the data generated from genome sequenc- vice S matching the request Q can be defined in a “useful” ing projects like the Human Genome Project is recognised way.
    [Show full text]
  • Ontology-Based Methods for Analyzing Life Science Data
    Habilitation a` Diriger des Recherches pr´esent´ee par Olivier Dameron Ontology-based methods for analyzing life science data Soutenue publiquement le 11 janvier 2016 devant le jury compos´ede Anita Burgun Professeur, Universit´eRen´eDescartes Paris Examinatrice Marie-Dominique Devignes Charg´eede recherches CNRS, LORIA Nancy Examinatrice Michel Dumontier Associate professor, Stanford University USA Rapporteur Christine Froidevaux Professeur, Universit´eParis Sud Rapporteure Fabien Gandon Directeur de recherches, Inria Sophia-Antipolis Rapporteur Anne Siegel Directrice de recherches CNRS, IRISA Rennes Examinatrice Alexandre Termier Professeur, Universit´ede Rennes 1 Examinateur 2 Contents 1 Introduction 9 1.1 Context ......................................... 10 1.2 Challenges . 11 1.3 Summary of the contributions . 14 1.4 Organization of the manuscript . 18 2 Reasoning based on hierarchies 21 2.1 Principle......................................... 21 2.1.1 RDF for describing data . 21 2.1.2 RDFS for describing types . 24 2.1.3 RDFS entailments . 26 2.1.4 Typical uses of RDFS entailments in life science . 26 2.1.5 Synthesis . 30 2.2 Case study: integrating diseases and pathways . 31 2.2.1 Context . 31 2.2.2 Objective . 32 2.2.3 Linking pathways and diseases using GO, KO and SNOMED-CT . 32 2.2.4 Querying associated diseases and pathways . 33 2.3 Methodology: Web services composition . 39 2.3.1 Context . 39 2.3.2 Objective . 40 2.3.3 Semantic compatibility of services parameters . 40 2.3.4 Algorithm for pairing services parameters . 40 2.4 Application: ontology-based query expansion with GO2PUB . 43 2.4.1 Context . 43 2.4.2 Objective .
    [Show full text]
  • Description Logics
    Description Logics Franz Baader1, Ian Horrocks2, and Ulrike Sattler2 1 Institut f¨urTheoretische Informatik, TU Dresden, Germany [email protected] 2 Department of Computer Science, University of Manchester, UK {horrocks,sattler}@cs.man.ac.uk Summary. In this chapter, we explain what description logics are and why they make good ontology languages. In particular, we introduce the description logic SHIQ, which has formed the basis of several well-known ontology languages, in- cluding OWL. We argue that, without the last decade of basic research in description logics, this family of knowledge representation languages could not have played such an important rˆolein this context. Description logic reasoning can be used both during the design phase, in order to improve the quality of ontologies, and in the deployment phase, in order to exploit the rich structure of ontologies and ontology based information. We discuss the extensions to SHIQ that are required for languages such as OWL and, finally, we sketch how novel reasoning services can support building DL knowledge bases. 1 Introduction The aim of this section is to give a brief introduction to description logics, and to argue why they are well-suited as ontology languages. In the remainder of the chapter we will put some flesh on this skeleton by providing more technical details with respect to the theory of description logics, and their relationship to state of the art ontology languages. More detail on these and other matters related to description logics can be found in [6]. Ontologies There have been many attempts to define what constitutes an ontology, per- haps the best known (at least amongst computer scientists) being due to Gruber: “an ontology is an explicit specification of a conceptualisation” [47].3 In this context, a conceptualisation means an abstract model of some aspect of the world, taking the form of a definition of the properties of important 3 This was later elaborated to “a formal specification of a shared conceptualisation” [21].
    [Show full text]
  • Proceedings of the 11Th International Workshop on Ontology
    Proceedings of the 11th International Workshop on Ontology Matching (OM-2016) Pavel Shvaiko, Jérôme Euzenat, Ernesto Jiménez-Ruiz, Michelle Cheatham, Oktie Hassanzadeh, Ryutaro Ichise To cite this version: Pavel Shvaiko, Jérôme Euzenat, Ernesto Jiménez-Ruiz, Michelle Cheatham, Oktie Hassanzadeh, et al.. Proceedings of the 11th International Workshop on Ontology Matching (OM-2016). Ontology matching workshop, Kobe, Japan. No commercial editor., pp.1-252, 2016. hal-01421835 HAL Id: hal-01421835 https://hal.inria.fr/hal-01421835 Submitted on 15 Jul 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Ontology Matching OM-2016 Proceedings of the ISWC Workshop Introduction Ontology matching1 is a key interoperability enabler for the semantic web, as well as a useful tactic in some classical data integration tasks dealing with the semantic hetero- geneity problem. It takes ontologies as input and determines as output an alignment, that is, a set of correspondences between the semantically related entities of those on- tologies. These correspondences can be used for various tasks, such as ontology merg- ing, data translation, query answering or navigation on the web of data. Thus, matching ontologies enables the knowledge and data expressed in the matched ontologies to in- teroperate.
    [Show full text]
  • Justification Oriented Proofs In
    Justification Oriented Proofs in OWL Matthew Horridge, Bijan Parsia, and Ulrike Sattler School of Computer Science, The University of Manchester Abstract. Justifications — that is, minimal entailing subsets of an on- tology — are currently the dominant form of explanation provided by ontology engineering environments, especially those focused on the Web Ontology Language (OWL). Despite this, there are naturally occurring justifications that can be very difficult to understand. In essence, justifi- cations are merely the premises of a proof and, as such, do not articulate the (often non-obvious) reasoning which connect those premises with the conclusion. This paper presents justification oriented proofs as a poten- tial solution to this problem. 1 Introduction and Motivation Modern ontology development environments such as Prot´eg´e-4, the NeOn Toolkit, Swoop, and Top Braid Composer, allow users to request explanations for entail- ments (inferences) that they encounter when editing or browsing ontologies. In- deed, the provision of explanation generating functionality is generally seen as being a vital component in such tools. Over the last few years, justifications have become the dominant form of explanation in these tools. This paper examines justifications as a kind of explanation and highlights some problems with them. It then presents justification lemmatisation as a non-standard reasoning service, which can be used to augment a justification with intermediate inference steps, and gives rise to a structure known as a justification oriented proof. Ultimately, a justification oriented proof could be used as an input into some presentation de- vice to help a person step though a justification that is otherwise too difficult for them to understand.
    [Show full text]
  • Curriculum Vitae
    Curriculum vitae Thomas Andreas Meyer 25 August 2019 Address Room 312, Computer Science Building University of Cape Town University Avenue, Rondebosch Tel: +27 12 650 5519 e-mail: [email protected] WWW: http://cs.uct.ac.za/~tmeyer Biographical information Date of birth: 14 January 1964, Randburg, South Africa. Marital status: Married to Louise Leenen. We have two children. Citizenship: Australian and South African. Qualifications 1. PhD (Computer Science), University of South Africa, Pretoria, South Africa, 1999. 2. MSc (Computer Science), Rand Afrikaans University (now the University of Johan- nesburg), Johannesburg, South Africa, 1986. 3. BSc Honours (Computer Science) with distinction, Rand Afrikaans University (now the University of Johannesburg), Johannesburg, South Africa, 1985. 4. BSc (Computer Science, Mathematical Statistics), Rand Afrikaans University (now the University of Johannesburg), Johannesburg, South Africa, 1984. 1 Employment and positions held 1. July 2015 to date: Professor, Department of Computer Science, University of Cape Town, Cape Town, South Africa. 2. July 2015 to June 2020: Director, Centre for Artificial Intelligence Research (CAIR), CSIR, Pretoria, South Africa. 3. July 2015 to June 2020: UCT-CSIR Chair in Artificial Intelligence, University of Cape Town, Cape Town, South Africa. 4. August 2011 to June 2015: Chief Scientist, CSIR Meraka Institute, Pretoria, South Africa. 5. May 2011 to June 2015: Director of the UKZN/CSIR Meraka Centre for Artificial Intelligence Research, CSIR and University of KwaZulu-Natal, South Africa. 6. August 2007 to July 2011: Principal Researcher, CSIR Meraka Institute, Pretoria, South Africa. 7. August 2007 to June 2015: Research Group Leader of the Knowledge Representation and Reasoning group (KRR) at the CSIR Meraka Institute, Pretoria, South Africa.
    [Show full text]
  • Owl2, Rif, Sparql1.1)
    http://www.csd.abdn.ac.uk/ http://www.deri.ie The Role of Logics and Logic Programming in Semantic Web Standards (OWL2, RIF, SPARQL1.1) Axel Polleres Digital Enterprise Research Institute (DERI) National University of Ireland, Galway 1 Outline ESWC2010 Quick intro of RDF/OWL/Linked Open Data OWL2 Overview: from OWL 1 to OWL 2 Reasoning services in OWL 2 OWL2 Treactable Fragments (OWL2RL, OWL2EL, OWL2QL) OWL2 and RIF OWL2 and SPARQL1.1 Time allowed: Implementing SPARQL, OWL2RL, RIF on top of DLV – The GiaBATA system 2 Example: Finding experts/reviewers? ESWC2010 Tim Berners-Lee, Dan Connolly, Lalana Kagal, Yosi Scharf, Jim Hendler: N3Logic: A logical framework for the World Wide Web. Theory and Practice of Logic Programming (TPLP), Volume 8, p249-269 Who are the right reviewers? Who has the right expertise? Which reviewers are in conflict? Observation: Most of the necessary data already on the Web, as RDF! More and more of it follows the Linked Data principles, i.e.: 1. Use URIs as names for things 2. Use HTTP dereferenceable URIs so that people can look up those names. 3. When someone looks up a URI, provide useful information. 4. Include links to other URIs so that they can discover more things. 3 RDF on the Web ESWC2010 (i) directly by the publishers (ii) by e.g. transformations, D2R, RDFa exporters, etc. FOAF/RDF linked from a home page: personal data (foaf:name, foaf:phone, etc.), relationships foaf:knows, rdfs:seeAlso ) 4 RDF on the Web ESWC2010 (i) directly by the publishers (ii) by e.g.
    [Show full text]
  • Table of Contents - Part II
    Table of Contents - Part II Semantic Web In-Use Track KOIOS: Utilizing Semantic Search for Easy-Access and Visualization of Structured Environmental Data 1 Veil Bicer, Thanh Tran, Andreas Abecker, and Radoslav Nedkov Wiki-Based Conceptual Modeling: An Experience with the Public Administration 17 Cristiano Casagni, Chiara Di Francescomarino, Mauro Dragoni, Licia Fiorentini, Luca Franci, Matteo Gerosa, Chiara Ghidini, Federica Rizzoli, Marco Rospocher, Anna Rovella, Luciano Serajini, Stefania Sparaco, and Alessandro Tabarroni Linking Semantic Desktop Data to the Web of Data 33 Laura Drägan, Renaud Delbru, Tudor Groza, Siegfried Handschuh, and Stefan Decker Linking Data across Universities: An Integrated Video Lectures Dataset 49 Miriam Fernandez, Mathieu d'Aquin, and Enrico Motta Mind Your Metadata: Exploiting Semantics for Configuration, Adaptation, and Provenance in Scientific Workflows 65 Yolanda Gil, Pedro Szekely, Sandra Villamizar, Thomas C. Harmon, Varun Ratnakar, Shubham Gupta, Maria Muslea, Fabio Silva, and Craig A. Knoblock Using Semantic Web Technologies to Build a Community-Driven Knowledge Curation Platform for the Skeletal Dysplasia Domain 81 Tudor Groza, Andreas Zankl, Yuan-Fang Li, and Jane Hunter Cyber Scientific Test Language 97 Peter Haglich, Robert Grimshaw, Steven Wilder, Marian Nodine, and Bryan Lyles How to "Make a Bridge to the New Town" Using OntoAccess 112 Matthias Hert, Giacomo Ghezzi, Michael Würsch, and Harald C. Gall The MetaLex Document Server: Legal Documents as Versioned Linked Data 128 Rinke Hoekstra Bibliografische
    [Show full text]
  • Data Complexity of Reasoning in Very Expressive Description Logics
    Data Complexity of Reasoning in Very Expressive Description Logics Ullrich Hustadt Boris Motik Ulrike Sattler Dept. of Computer Science Forschungszentrum Informatik Dept. of Computer Science Univ. of Liverpool, UK Univ. of Karlsruhe, Germany Univ. of Manchester, UK [email protected] [email protected] [email protected] Abstract reasoning problems are P-complete in |A|. To develop an intuition and to provide a more detailed account of these re- Data complexity of reasoning in description logics sults, we compare them with similar results for (variants of) (DLs) estimates the performance of reasoning al- datalog [Dantsin et al., 2001]. gorithms measured in the size of the ABox only. Our results are important since they provide a formal justi- We show that, even for the very expressive DL fication for hoping to provide tractable algorithms for very ex- SHIQ, satisfiability checking is data complete for pressive description logics. Furthermore, Horn-SHIQ sub- NP. For applications with large ABoxes, this can sumes DL-lite [Calvanese et al., 2004], a logic aiming to be a more accurate estimate than the usually con- capture most constructs of ER and UML formalisms, while sidered combined complexity, which is EXPTIME- providing polynomial algorithms for satisfiability checking complete. Furthermore, we identify an expressive and conjunctive query answering (assuming an unbounded fragment, Horn-SHIQ, which is data complete for knowledge base, but a bound on the query size). Horn- P, thus being very appealing for practical usage. SHIQ additionally allows qualified existential quantifica- tion, conditional functionality and role inclusions, while al- 1 Introdcution lowing for a reasoning algorithm that runs in time polynomial Description logics (DLs) [Baader et al., 2003] are state-of- in the size of data.
    [Show full text]
  • Justification Masking In
    Proc. 23rd Int. Workshop on Description Logics (DL2010), CEUR-WS 573, Waterloo, Canada, 2010. Justification Masking in OWL Matthew Horridge1, Bijan Parsia1, Ulrike Sattler1 The University of Manchester, UK Abstract. This paper presents a discussion on the phenomena of mask- ing in the context of justifications for entailments. Various types of mask- ing are introduced and a definition for each type is given. 1 Introduction Many open source and commercial ontology development tools such as Prot´eg´e- 4, Swoop, The NeOn Toolkit and Top Braid Composer use justifications [5] as a kind of explanation for entailments in ontologies. A justification for an entail- ment, also known as a MinA [1, 2], or a MUPS [11] if specific to explaining why a class name is unsatisfiable, is a minimal subset of an ontology that is sufficient for the given entailment to hold. More precisely, a justification is taken to be a subset minimal set of axioms that supports an entailment. Justifications are a popular in the OWL world and, as the widespread tooling support shows, have been used in preference to full blown proofs for explaining why an entailment follows from a set of axioms. However, despite the popularity of justifications, they suffer from several problems. Some of these problems, namely issues arising from the potential su- perfluity of axioms in justifications, were highlighted in [3]. Specifically, while all of the axioms in a justification are needed to support the entailment in question, there may be parts of these axioms that are not required for the entailment to hold. For example, consider J = {A ⊑ ∃R.B, Domain(R, C),C ⊑ D ⊓E} which entails A ⊑ D.
    [Show full text]
  • Empirical Study of Logic-Based Modules: Cheap Is Cheerful
    Empirical Study of Logic-Based Modules: Cheap Is Cheerful Chiara Del Vescovo1, Pavel Klinov2, Bijan Parsia1, Ulrike Sattler1, Thomas Schneider3, and Dmitry Tsarkov1 1 University of Manchester, UK {delvescc|bparsia|sattler|tsarkov}@cs.man.ac.uk 2 University of Ulm, Germany [email protected] 3 Universit¨atBremen, Germany [email protected] Abstract. For ontology reuse and integration, a number of approaches have been devised that aim at identifying modules, i.e., suitably small sets of \relevant" axioms from ontologies. Here we consider three logically sound notions of modules: MEX modules, only applicable to inexpressive ontologies; modules based on semantic locality, a sound approximation of the first; and modules based on syntactic locality, a sound approximation of the second (and thus the first), widely used since these modules can be extracted from OWL DL ontologies in time polynomial in the size of the ontology. In this paper we investigate the quality of both approximations over a large corpus of ontologies, using our own implementation of seman- tic locality, which is the first to our knowledge. In particular, we show with statistical significance that, in most cases, there is no difference between the two module notions based on locality; where they differ, the additional axioms can either be easily ruled out or their number is relatively small. We classify the axioms that explain the rare differences into four kinds of \culprits" and discuss which of those can be avoided by extending the definition of syntactic locality. Finally, we show that differences between MEX and locality-based modules occur for a minor- ity of ontologies from our corpus and largely affect (approximations of) expressive ontologies { this conclusion relies on a much larger and more diverse sample than existing comparisons between MEX and syntactic locality-based modules.
    [Show full text]