University of Pennsylvania ScholarlyCommons
Technical Reports (CIS) Department of Computer & Information Science
November 2007
Integrating Ontologies and Relational Data
Sören Auer University of Pennsylvania, [email protected]
Zachary G. Ives University of Pennsylvania, [email protected]
Follow this and additional works at: https://repository.upenn.edu/cis_reports
Recommended Citation Sören Auer and Zachary G. Ives, "Integrating Ontologies and Relational Data", . November 2007.
University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-07-24.
This paper is posted at ScholarlyCommons. https://repository.upenn.edu/cis_reports/716 For more information, please contact [email protected]. Integrating Ontologies and Relational Data
Abstract In recent years, an increasing number of scientific and other domains have attempted to standardize their terminology and provide reasoning capabilities through ontologies, in order to facilitate data exchange. This has spurred research into Web-based languages, formalisms, and especially query systems based on ontologies.
Yet we argue that DBMS techniques can be extended to provide many of the same capabilities, with benefits in scalability and performance. We present OWLDB, a lightweight and extensible approach for the integration of relational databases and description logic based ontologies. One of the key differences between relational databases and ontologies is the high degree of implicit information contained in ontologies. OWLDB integrates the two schemes by codifying ontologies' implicit information using a set of sound and complete inference rules for SHOIN (the description logic behind OWL ontologies. These inference rules can be translated into queries on a relational DBMS instance, and the query results (representing inferences) can be added back to this database. Subsequently, database applications can make direct use of this inferred, previously implicit knowledge, e.g., in the annotation of biomedical databases. As our experimental comparison to a native description logic reasoner and a triple store shows, OWLDB provides significantly greater scalability and query capabilities, without sacrifcing performance with respect to inference.
Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MS- CIS-07-24.
This technical report is available at ScholarlyCommons: https://repository.upenn.edu/cis_reports/716 Integrating Ontologies and Relational Data
Sören Auer Zachary Ives Computer and Information Science Computer and Information Science University of Pennsylvania University of Pennsylvania Philadelphia, PA 19104, USA Philadelphia, PA 19104, USA [email protected] [email protected]
ABSTRACT facts by running in polynomial data complexity, the descrip- In recent years, an increasing number of scientific and other tion logics used to define ontologies are a different subset domains have attempted to standardize their terminology that allows richer specification of classes and relationships, and provide reasoning capabilities through ontologies, in or- but is less computationally tractable. Both approaches have der to facilitate data exchange. This has spurred research a role in encoding and sharing information today, and in into Web-based languages, formalisms, and especially query fact the two worlds are increasingly being interconnected: systems based on ontologies. Bioinformatics data is generally represented in a variety of Yet we argue that DBMS techniques can be extended databases, which categorize the data entries by referenc- to provide many of the same capabilities, with benefits in ing classes in the Open Biomedical Ontologies (OBO) [25]; scalability and performance. We present OWLDB, a light- anatomical measurements are stored in databases that then weight and extensible approach for the integration of rela- reference the Foundational Model of Anatomy [22]; prod- tional databases and description logic based ontologies. One ucts in e-commerce reference categories in eClassOWL [15]; of the key differences between relational databases and on- personal information management systems need class and tologies is the high degree of implicit information contained relationship information such as that in FOAF [9]. Hence, in ontologies. OWLDB integrates the two schemes by cod- ontology and database integration is already a problem to- ifying ontologies’ implicit information using a set of sound day — it will be even more so if the Semantic Web is to and complete inference rules for SHOIN – the description succeed today’s Web. logic behind OWL ontologies. These inference rules can be As we begin to integrate systems based on these disparate translated into queries on a relational DBMS instance, and formalisms, a natural question arises about which architec- the query results (representing inferences) can be added back ture to use: a mediator that partitions computations across to this database. Subsequently, database applications can independent database and ontology-based systems, a single make direct use of this inferred, previously implicit knowl- system that extends a description logics engine to include edge, e.g., in the annotation of biomedical databases. As database query capabilities, or a database engine extended our experimental comparison to a native description logic with certain description logics reasoning capabilities. Our reasoner and a triple store shows, OWLDB provides signif- thesis in this paper is that the third approach — a single icantly greater scalability and query capabilities, without reasoning engine that builds upon database query process- sacrificing performance with respect to inference. ing capabilities — is the most useful, as we explain and then validate. Systems developed for description logic reasoning focus 1. INTRODUCTION mainly on three basic capabilities: The problem of encoding information in a standardized way has been a challenge addressed in different ways by dif- • subsumption reasoning, i.e. the inference of implicit ferent communities. In the database world, entity-relationship subclass-superclass relationships, models, inheritance, and declarative views are the basic mech- • satisfiability and consistency checks, i.e. whether a anisms for expressing concepts and their relationships. An class can potentially have instances; if not, whether alternative approach has been adopted by the knowledge there is a contradiction with explicitly defined ones, representation community, namely ontologies and descrip- tion logics. In contrast to database formalisms, which focus • classification of objects, i.e. the determination of class on a subset of first-order logic that scales to large numbers of membership for objects or the retrieval of all instances of a certain class.
They are generally optimized for fairly complex reasoning about relatively few facts. Permission to make digital or hard copies of all or part of this work for Unfortunately, with the adoption of ontologies in science, personal or classroom use is granted without fee provided that copies are we are increasingly encountering the challenges of scale, both not made or distributed for profit or commercial advantage and that copies in terms of large amount of instance data and large numbers bear this notice and the full citation on the first page. To copy otherwise, to of concepts. For instance, the WordNet linguistic ontol- republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. ogy includes 100,000 concepts and the NCI cancer ontology Copyright 200X ACM X-XXXXX-XX-X/XX/XX ...$5.00. has 30,000 classes; biomedical data from different sources adopt a variety of ontologies (e.g., OBO [25], FMA [22], MicroOrganism MGED [33]). In contrast to the assumptions of description logics reasoners, these ontologies have large, relatively sim- ple terminological parts (i.e., concept and role definitions), InfectiveAgent ≡ MicroOrganism u ∃isCausalAgentOf.Infection Bacterium and an even larger number of data instances. Ontologies such as the NCI cancer ontology exceed the capabilities of most current description logics reasoners. This inadequacy A-Box … MicroOrg123 has been observed by a number of authors (e.g. [37, 30, 16]). … InfectiveAgent123 isCausalAgentOf:Infect123 Bacter123 Some efforts have been made to employ databases to per- … form limited tasks to assist description logics reasoners (e.g. Subsumption: explicit inferred instanceOf: explicit inferred [8, 6]), using the reasoner to perform reasoning about classes and roles and the DBMS to reason about data. However, Figure 1: Subsumption and classification in a bio- it has been shown that the full power of certain common medical ontology. description logics can be expressed using disjunctive data- log [17], and we argue that the best approach in many set- tings is to perform almost all of the reasoning in the DBMS, Description logic. Description logics are decidable frag- thus avoiding the overhead implicit in coupling systems. We ments of first order logic. They represent knowledge in terms exploit the fact that most large real-world ontologies do not of objects, concepts, and roles. Objects correspond to con- use arbitrarily complex and unique representation methods stants, concepts to unary predicates, and roles to binary for every single class definition: rather, they define many predicates in first order logic. In Description Logic systems similar classes that can be reasoned about “in bulk,” and information is stored in a knowledge base, which is a set of the strengths of DBMS query processing are more suited axioms. It is divided in two parts: TBox and ABox. The for such tasks. This is especially useful because most de- ABox contains assertions about objects. It relates objects scription logics reasoners already use database technology to concepts and roles. The TBox describes the terminology to store data instances, and since our goal is to combine by relating concepts and roles. ontology and database data under a single query interface. The description logic SHOIN . We briefly introduce We make the following contributions: the SHOIN description logic, which is the base language for OWL DL ontologies and refer to [3] for further back- • a methodology for translating SHOIN inference rules ground on description logics. The syntax and semantics of into relational database queries, SHOIN concept constructors is shown in Table 1. As usual in logics, interpretations are used to assign a meaning to • a database schema and encoding scheme for high per- syntactic constructs. An interpretation I consists of a non- formance inferencing by means of the derived queries, empty interpretation domain ∆I and an interpretation func- I • stratification policies for the OWL inference rules, al- tion · , which assigns to each object o (symbolized by ovals in the example depicted in Figure 1) an element of ∆I , to lowing for efficient execution within a fixpoint algo- I I rithm executing in middleware above a DBMS. each concept name c (symbolized by squares) a set c ⊆ ∆ , and to each role r (symbolized by arrows) a binary relation This paper is structured as follows. We provide an overview rI ⊆ ∆I × ∆I . Interpretations are extended from elements of the description logic SHOIN in Section 2. Section 3 de- to concepts as shown in Table 1, and to other elements of a scribes the concept of description logic reasoning by means knowledge base in a straightforward way. An interpretation of inference rules and how suitable inference rules can be that satisfies an axiom (set of axioms) is called a model of obtained. Section 4 presents our scheme for reasoning (in- this axiom (set of axioms). ference) using a“thin”middleware layer over an SQL DBMS. Inference tasks. Inference algorithms extract implicit We experimentally validate our scheme in Section 5, discuss knowledge from a given knowledge base. Standard reason- related work in Section 6, and conclude in Section 7. ing tasks include instance checks, consistency checks and subsumption. We explicitly define the last: Let c1, c2 be concepts and T a TBox. c1 is subsumed by c2, denoted by 2. PRELIMINARIES I I c1 v c2, iff for any interpretation I we have c1 ⊆ c2. c1 is Web Ontology Language. The Web Ontology Lan- subsumed by c2 with respect to T (denoted by c1 vT c2) iff guage OWL is a semantic markup language for publishing I I for any model I of T we have c1 ⊆ c2. c1 is equivalent to and sharing ontologies on the World Wide Web [5]. It is c2 (with respect to T ), denoted by c1 ≡ c2 (c1 ≡T c2), iff an established standard and widely used in applications in c1 v c2 (c1 vT c2) and c2 v c1 (c2 vT c1). science and increasingly often also in industry. OWL is de- Computing the subsumption relation between concepts is veloped as a vocabulary extension of RDF (the Resource a key to render other reasoning services as well: Description Framework) [19]. Hence, OWL ontologies are encoded as statements adhering to the subject-predicate- • Instance checks (used for query answering): if c1 is object data model of RDF (see the OWL/XML example subsumed by c2, all instances of c1 will be also instan- column in Table 1). OWL has three increasingly-expressive tiations of c2. sublanguages: OWL Lite, OWL DL, and OWL Full. While • Consistency: a knowledge base is inconsistent, if a OWL Lite is not expressive enough for many applications, class c is known to be subsumed by the bottom concept OWL Full (the most expressive sublanguage) provides no ⊥ and contains an instance. computational guarantees. However, OWL DL (where DL stands for Description Logic) provides high expressiveness Example. The reasoning tasks subsumption and instance while retaining computational tractability. check and their interrelation is illustrated in Figure 1 with Constructor name Syntax Semantics OWL/RDF example atomic concept a aI ⊆ ∆I role r rI ⊆ ∆I × ∆I individual o oI ∈ ∆I top concept > >I = ∆I owl:Thing bottom concept ⊥ ⊥I = ∅ owl:Nothing inverse role r− (r−)I = (rI )− r1 owl:inverseOf r2 I I I conjunction c1 u c2 (c1 u c2) = c1 ∩ c2 c owl:intersectionOf rdflist I I I disjunction c1 t c2 (c1 t c2) = c1 ∪ c2 c owl:unionOf rdflist negation ¬c (¬c)I = ∆I \ cI c1 owl:complementOf c I I oneOf {o1,... } ({o1,... }) = {o1,... } c owl:oneOf rdflist exists restriction ∃r.c (∃r.c)I = {x|∃y : hx, yi ∈ rI and y ∈ cI } c1 owl:someValuesFrom c value restriction ∀r.c (∀r.c)I = {x|∃y : hx, yi ∈ rI → y ∈ cI } c1 owl:allValuesFrom c atleast restriction ≥ nr (≥ nr)I = {x|#({y : hx, yi ∈ rI }) ≥ n} c owl:minCardinality n atmost restriction ≤ nr (≤ nr)I = {x|#({y : hx, yi ∈ rI }) ≤ n} c owl:maxCardinality n Axiom Name Syntax Semantics OWL/RDF example I I concept inclusion c1 v c2 c1 ⊆ c2 c1 rdfs:subClassOf c2 I I role inclusion r1 v r2 r1 ⊆ r2 r1 rdfs:subPropertyOf r2 role transitivity r ≡ r+ rI = (rI )+ r rdf:type owl:TransitiveProperty role symmetry r ≡ r− rI = (rI )− r rdf:type owl:symmetricProperty individual inclusion o : c oI ∈ CI o rdf:type c I I individual equality o1 = o2 o1 = o2 o1 owl:sameAs o2 I I individual inequality o1 6= o2 o1 6= o2 o1 owl:differentFrom o2
Table 1: Syntax and semantics of SHOIN and RDF examples (we use the common RDF, RDF-Schema and OWL namespace prefixes and assume a default namespace defined; rdflist refers to an RDF resource representing an RDF list containing the constituents of the union, intersection or exhaustive enumeration).
an example from the Galen medical terminology ontology c = c1 u c2), we can easily infer that c is a subclass of c1 [31]. After inferring that InfectiveAgent is subsumed by the as well as of c2 (c v c1 and c v c2). Similarly, from class class MicroOrganism the instance InfectiveAgent123 will also definitions P arent = (≥ 1hasChild) and LuckyP arent = instantiate MicroOrganism. A similar inference can be made (≥ 2hasChild) we can infer LuckyP arent v P arent. for the instance Bacter123, however, here the subsumption However, in addition to deriving sound inference rules it is relation between Bacterium and MicroOrganism is already crucial to describe the fragment of a description logic covered explicit. The conclusion that MicroOrg123 is an instance by the inference rules, i.e., the fragment for which complete- of InfectiveAgent, on the other hand, can not be reduced to ness of the inferences can be guaranteed. Not surprisingly, subsumption, but can be decided by checking the member- a great deal of theoretical work has been done in these ar- ship of MicroOrg123 with respect to every constituent of the eas. We base our OWLDB implementation on the theoreti- intersection serving as a definition for InfectiveAgent. cal foundations of [28] and the KIT report 111 [29] (both by Royer and Quantz). Royer and Quantz systematically de- rive a complete set of inference rules for a description logic 3. DERIVING INFERENCE RULES FOR ON- that happens to subsume SHOIN (the description logic be- TOLOGIES hind OWL); their work is purely from a definitional per- Description logic reasoners approach the problem of decid- spective and does not consider an implementation. They ing subsumption between two classes by reducing the prob- develop sound and complete Sequent Calculi axiomatiza- tions of First-Order Logic without (FOL) or with Equality lem to a consistency check: For classes c1 and c2, c1 v c2 can be decided by checking the consistency of KB = {o : c, c ≡ (FOL=). A general methodology for obtaining sound and complete inference systems for any logical language L is to c1 u ¬c2}. Consistency is often decided by trying to con- struct a model by means of so called tableau algorithms [4]. translate the formulae of L (L-formulae) into first-order for- This method is time-tested and has proven to be sound and mulae (provided L is translatable into FOL), and then to complete for most description logics. However, in reason- identify necessary and sufficient conditions of provability in ing about subsumption with many classes, it requires high Sequent Calculi of the FOL translations from the formu- numbers of computation steps, and worse, large in-memory lae encoding L-formulae. The extensive analysis of Sequent state. In order to scale to such ontologies, we instead exe- Calculi proofs by Royer and Quantz resulted in a set of 168 cute inference rules for description logics by codifying them inference rules. However, it is important to note that the as relational database queries. DL consider in the KIT report differs from SHOIN , in the It is easy to intuitively derive some sound inference rules following ways: from the set based semantics of the SHOIN class and prop- erty constructors or axioms as shown in Table 1. For exam- • It supports the complex role constructors: r1 t r2 (role ple, from the definition of a class c to contain exactly the union), r1 u r2 (role intersection), r1 ∗ r2 (role compo- instances within the intersection of classes c1 and c2 (i.e. sition), ¬r role complement. To close the constructors with respect to union and intersection the DL also in- Conjunction and Disjunction r cludes a top (>r) and bottom role (⊥ ). → c v c (1) • It supports qualified cardinality restrictions (notation → c1 u c2 v c1 t c3 (2) (≥ nr.c) and (≤ nr.c)), stating that objects belonging c1 v c2 → c1 u c3 v c2 (3) to the restriction must have a maximum or minimum c1 v c2 → c1 v c2 t c3 (4) number of role values of a certain type. SHOIN , on c1 v c2, c1 v c3 ↔ c1 v c2 u c3 (5) the other hand, supports only unqualified number re- c2 v c1, c3 v c1 ↔ c2 t c3 v c1 (6) strictions ((≥ nr) and (≤ nr)), where the type of the c1 v c2, c2 u c3 v c4 → c1 u c3 v c4 (7) role values is not important. → ⊥ v c (8) → c v > (9) • A class restriction ‘fills’ (notation r.{o1, . . . , on}) is Quantification supported, requiring all instances of the restriction to be related to all the values of the filler ({o1, . . . , on}). > v c ↔ > v ∀r.c (10) In the special case that the filler contains just one ob- c v ⊥ ↔ ∃r.c v ⊥ (11) ject (i.e. r.{o}) the restriction is equivalent to the ex- c1 v c2, r2 v r1 → ∀r1.c1 v ∀r2.c2 (12) ists restriction ∃r.{o}. c1 v c2, r1 v r2 → ∃r1.c1 v ∃r2.c2 (13) c2 u c1 v ⊥, r1 v r2 → ∀r2.c2 u ∃r1.c1 v ⊥ (14) • The domain (or range) of roles is defined by restrict- > v c2 t c1, r1 v r2 → > v ∃r2.c2 t ∀r1.c1 (15) ing a general role r to a role c|r (or r|c), whose do- c1 u c2 v c3, r3 v r1, r3 v r2 → ∀r1.c1 u ∀r2.c2 v ∀r3.c3 (16) main (or range) contains exactly only instances of c. c3 v c1 t c2, r3 v r1, r3 v r2 → ∃r3.c3 v ∃r1.c1 t ∃r2.c2 (17) In SHOIN on the other hand a domain (or range) def- c1 u c2 v c3, r2 v r1, r2 v r3 → ∀r1.c1 u ∃r2.c2 v ∃r3.c3 (18) inition for a role is ‘emulated’ by an axiom (≥ 1r) v c c3 v c1 t c2, r2 v r1, r2 v r3 → ∀r3.c3 v ∃r1.c1 t ∀r2.c2 (19) (or > v ∀r.c). Negation Hence, the DL regarded in the KIT report clearly sub- → c u ¬c v ⊥ (20) sumes SHOIN and to obtain a subset of inference rules for → > v c t ¬c (21) SHOIN we can (a) omit the KIT rules dealing with com- c1 u c2 v c3 ↔ c1 v c3 t ¬c2 (22) plex role constructors as well as domain and range restric- c1 v c2 t c3 ↔ c1 u ¬c2 v c3 (23) tions (since they are not derivable for SHOIN ), (b) derive → ¬¬c ≡ c (24) rules with unqualified cardinality restrictions from the ones → ¬(c1 u c2) ≡ ¬c1 t ¬c2 (25) with qualified cardinality restrictions by replacing the qual- → ¬(c1 t c2) ≡ ¬c1 u ¬c2 (26) ification class with the top concept (>) and (c) replace ‘fills’ → ¬∃r.c ≡ ∀r.¬c (27) restrictions in rules with exists restrictions. As a conse- → ¬∀r.c ≡ ∃r.¬c (28) quence of the simplification in (b) and (c) some rules (such Cardinality Restrictions as rule 48 in the KIT report) turn out to be redundant and can be omitted. This reduces the 168 KIT rules to 66, as c v ⊥ → > v (≤ nr) (29) shown in Figures 2 and 3. Rules 1-47 correspond to the rules c v ⊥ → (≥ nr) v ⊥ (30) with the same numbers in the KIT report. As a result of → (≥ 1r) ≡ ∃r.> (31) the systematic and complete derivation of inference rules in → (≥ 1r) ≡ ¬∀r.⊥ (32) the KIT report [29] and the rule adaptation to SHOIN we → (≤ 0r) ≡ ∀r.⊥ (33) obtain the following proposition: → (≤ 0r) ≡ ¬∃r.> (34) m = n − 1 → ¬(≥ nr) ≡ (≤ mr) (35) Proposition 1. The inference rules 1-55 (as shown in m = n + 1 → ¬(≤ nr) ≡ (≥ mr) (36) Figures 2 and 3) are sound and complete with respect to q ≤ p, r1 v r2 → (≥ pr1) v (≥ qr2) (37) class and role subsumption reasoning in SHOIN . q < p, r1 v r2 → (≤ qr2) u (≥ pr1) v ⊥ (38) q < p, r1 v r2 → > v (≥ qr2) t (≤ pr1) (39) Proof. The KIT rules are derived by translating all pos- p ≤ q, r2 v r1 → (≤ pr1) v (≤ qr2) (40) sible subsumption and instance recognition formulae of the r1 v r2 → (≥ nr1) u ∀r2.⊥ v ⊥ (41) KIT description logic into first-order formulae, and then to q < p, r1 v r2, r1 v r3 → (≤ qr2) u (≥ pr1) u ∀r3.c v ⊥ (42) identify necessary and sufficient conditions of provability in q ≤ p, r1 v r2, r1 v r3 → (≥ pr1) u ∀r3.c v (≥ qr2) (43) Sequent Calculi of the FOL translations. This method is q ≤ p, r1 v r2, r1 v r3 → (≤ qr2) u ∀r3.c v (≤ pr1) (44) clearly monotonic, i.e. a subsumed, less expressive descrip- r1 v r2 → (≥ nr1) u (≤ nr2) v > (45) i=k tion logic will result in a subset of possible subsumption and X instance recognition formulae and consequently a subset of (pi) < n, r v ri → (≥ nr) u (≤ p1r1) u ... (46) derivable inference rules. Hence, it is safe to omit KIT rules i=1 u(≤ pkrk) v ⊥ containing language constructs which are not available in r v r1, r v r2 → (≤ pr1) u (≤ qr2) v (≤ p+qr) (47) SHOIN and reduce the more general language constructs OneOf (qualified number restrictions and fills) to the specialized equivalents in SHOIN : S ⊆ T → S v T (48) Rules 1-28 are the same as in the KIT report. Rules 29- → S u T ≡ {S ∩ T } (49) 47 are derived by replacing qualified cardinality restrictions n ≥ |S|, r2 v r1 → ∀r1.S v (≤ nr2) (50) with unqualified cardinality restrictions. After doing so in KIT rule 48, this rule turns out to be equivalent to rule 38. Figure 2: SHOIN class subsumption inference rules. KIT rules 51, 52 and 55, 56, 101, 103, 117 are the same Role Subsumption and Inversion models namespaces
→ r v r (51) PK id PK id − − r1 v r2 → r1 v r2 (52) → r−− ≡ r (53) modelURI ns − − statements baseURI r1 v r2 → r1 v r2 (54) − − r1 v r2 → r1 v r2 (55) resources lists Instance recognition modelID subject PK id PK id predicate a : c1, c1 v c2 → a : c2 (56) object ns member → a : > (57) object_is name member_is a : c1, a : c2 ↔ a : c1 u c2 (58) a ∈ S → a : S (59) literals restrictions a∈ / S → a : ¬S (60) PK id PK subject a1 : ∀r.c, a1 : r.{a2} → a2 : c (61) a1 : ∀r.c, a2 : ¬c → a1 : ¬(r.{a2}) (62) value property a1 : r.{a2}, a2 : c → a1 : ∃r.c (63) language value a1 : r.{a2}, > v ∀r.c → a2 : c (64) datatype type a1 : r.{a2}, (≥ 1r) v c → a1 : c (65) − a1 : r.{a2} → a2 :(r : a1) (66) Figure 4: Database schema for RDF storage, opti- mized for the execution of inference rules. Figure 3: SHOIN role subsumption, inversion and instance recognition inference rules. been proposed. The central element of most of these is a table capturing the subject-predicate-object statements and as 48, 49 and 50, 51, 52, 54, 55. KIT rules 102, 104 are optionally additional tables for normalization, replication, equivalent to rule 53. The following KIT rules will not be caching purposes. During our extensive experiments with derivable for SHOIN : 49, 57-100, 131-156 (due to usage of OWLDB, we developed a scheme that sped up queries and complex roles constructors), 50, 53, 54 (qualified cardinality insertions by de-normalizing several relations, with 30-50% restriction which can not be replaced by top concept, since increased storage space requirements. OWLDB makes infer- the qualification class is required to be an oneOf class). ences by executing queries and making insertions into tables; hence insertion performance is the key bottleneck. Insertions However, the rules are incomplete with respect to instance over better-normalized schemes are comparably slow due to recognition, and consequently also not sufficient to detect checks for existence of identifiers in the normalization tables. inconsistencies with respect to objects being instances of Although the presented approach does not require a spe- unsatisfiable classes. The incompleteness with respect to cific relational schema (whether normalized or unnormal- instance recognition is due to missing rules for case reason- ized), the one depicted in Figure 4 performed best on our ing. Case reasoning would be required to handle rules with tests. In this database schema, each RDF triple corresponds disjunctions in the consequent, such as: to a row in the table statements referencing RDF resources and literals in the subject, predicate and object columns o : ∀r.{o1, . . . , on}, o : ∃r.c → o1 : c ∨ · · · ∨ on : c from respective tables (the binary values of the column objects_is indicates whether the object column references a resource or Because by the notorious complexity of deriving case rea- literal). The modeID enables the storage of multible ontolo- soning rules and standard databases being ill-suited to han- gies (models) within one relational schema. For simplicity dle such disjunctions efficiently we decided not to extend our we omit constraints on this column in the example queries approach in that direction. below. The two helper tables lists and restrictions repli- cate information with respect to RDF lists and OWL restric- 4. ONTOLOGY REASONING WITH A RE- tions from the statements table to speed-up query execu- LATIONAL DATABASE tion. As a consequence, the restrictions table contains In order to exploit the indexing and query optimization one row for each restriction with either one of the types techniques available in relational databases for the execu- minCardinality, maxCardinality, cardinality, hasValue, tion of the inference rules we present in this section a stor- someValuesFrom, allValuesFrom. age schema for OWL ontologies optimized for inference rule execution, we demonstrate how the inference rules can be 4.2 Translating Inference Rules into Database translated into queries on this schema and exhibit an algo- Queries rithm for efficiently executing these queries. After we derived inference rules for the description logic SHOIN and we are able to store SHOIN ontologies in a 4.1 Ontology Storage in Relational Databases relational database, we would like to employ these rules for Due to the standardized representation of OWL ontologies computing appropriate inferences. Each one of the rules can in RDF, which consists of subject-object-predicate tuples, it be translated into one or multiple corresponding SQL queries is common to store OWL ontologies within a ternary rela- on the ontology storage schema. The general method is to tional DBMS table. (See Table 1 to see how SHOIN axioms translate all premises of a rule, as well as requirements on can be represented as RDF statements). A variety of dif- the structure of the subsumed and subsuming class in the ferent relational schema to store such RDF statements has consequent into joins and join conditions on tables of the RDF storage schema. Query optimization techniques devel- faced the following, rather technical challenges during the oped for database systems will lead to the identification of translation: those conditions which restrict the result set most and hence can be evaluated fastest; data indexing makes sure matching • The inference rules contain only binary intersections classes are retrieved fast. The generated SQL queries select and unions. For OWL ontologies, however, the union exactly two classes (two roles or an instance and a class) for or intersection operator is applied to an arbitrarily long which a subclass-superclass (subrole-superrole or type) rela- list of objects (as stored in the lists table). Hence, tionship can be inferred. The result of these queries can be the resulting SQL queries must handle unions and in- added back to the database in the form of triples or stored tersections with arbitrary numbers of constituents. in separate tables for faster querying or deletion in case of ontology changes. • Some rules are bi-directional (i.e. support inferences We demonstrate the method on the example of rule 37: in both directions), some state the equivalence of two objects (i.e. c1 ≡ c2 ⇔ c1 v c2, c2 v c1). We had to q ≤ p, r1 v r2 → (≥ pr1) v (≥ qr2) split each of those into two separate rules.
An equivalent denotation is: • The OWL embedding in the RDF subject-predicate-
c1 = (≥ pr1), c2 = (≥ qr2), q ≤ p, r1 v r2 → c1 v c2 object data model, which served as a basis for the stor- age schema, defines a number of shortcuts for express- Each of the conjuncts in the premise of this rule can be ing certain axioms, i.e.
MGED ALCOF(D) 234 162 709 0.41 700 Galen SHF 2749 413 0 2.33 600 SUMO ALH(D) 630 246 435 0.46 500 eClassOWL ALH(D) 76976 5529 4544 25.4 400 300 Time (s) UOBDL1 0.05M 23 200 UOBDL5 SHOIN(D) 69 47 0.2M 100 100 0 UOBDL10 1.2M 196 Wine Wine2 Wine3 Wine4 Wine5 Wine6 Wine7 Wine8 Wine9 Wine10 Pellet 32.47 96.98 263.07 649.01 Table 2: Expressiveness and sizes of benchmark on- OWLDB 4.22 9.6 15.24 22.72 31.31 41.97 53.17 65.15 78.35 88.79 tologies. Figure 5: Scalability of subsumption for Pellet and Wine Ontology is the example ontology accompany- OWLDB for the Wine ontology in different sizes. ing the official W3C OWL standard. To exhibit the OWL features, it exemplary demonstrates their usage in the do- The measured results show that OWLDB’s execution time main of wine and food. Due to the comprehensive and bal- grows significantly slower than Pellet’s for increasing on- anced usage of different OWL expressions, the Wine Ontol- tology sizes. Furthermore, Pellet’s desire for main mem- ogy qualifies as an indicator for the grade of OWL support. ory exceeds the available resources starting from Wine5. Further, when used as prototype for ontologies of larger size This need for main memory limits the amount of poten- (by cloning resources), these can be expected to give mean- tially processable OWL ontologies for Pellet (and, we conjec- ingful insights into the scalability properties of a reasoning ture, most tableau algorithm based reasoners) dramatically. algorithm. However, the MySQL process executing OWLDB’s queries Pellet OWLDB OBO Pathway 797 600 OBO MolFunc 185375 4119 OBO BioProc 424937 36427 MGED 280905 738 Galen 36080 4140271 SUMO 1032 1018 eClass- OWL 10000000 6239
OBO Mesh 1346 uninteressant OBO Mouse Pathology 430 uninteressant NCI uninteressant Tambisuses a small (less than1750 50MB) and988 constant amount of main is better integrated in OWLIM. Furthermore, OWLIM memory independent of the ontology size. Consequently, works solely in main memory which at this point sig- OWLDB is able to process potentially all OWL ontologies nificantly contributes to better performance. as long as execution time is not limited. In Figure 6, the subsumption calculation time of OWLDB • OWLDB evaluates more OWL expressions (such as and Pellet is presented for various ontologies of different arbitrary cardinality restrictions) than OWLIM and sizes, using different OWL features. hence needs more time to perform the required infer- ences. 10000000 • The currently used DBMS MySQL does not provide 1000000 Loadtime optimizationsSesame DL1 OWLDB for computing DL1 Sesame DL5 transitiveOWLDB DL5 closures.Sesame DL1 In0OWLDB DL10 100000 Pars.+Load.+UOBI the24.00 calculation of the119.00 property extent for the276 Parsing 7.16 28.60 55.22 10000 Loading transitive property uob:hasSameHomeTownWith3.78 16.93 alone ac- 37.78 Inferencingcounts for 30-60%84.00 of OWLDB’s overall220.00 ABox infer- 678.00 1000 ence time (cf. also Section 5.5). Hence, OWLDB will 100 profit significantly when the SQL99 features for recur-
Time (ms) 10 sive queries are available and data access is optimized
1 accordingly. OBO OBO OBO eClass- Literals 0,44 1,8 3,5 MGED Galen SUMO Namespaces 0,13 0,8 0,2 Pathway MolFunc BioProc OWL In general, load times have much less importance for the Pellet 797 185375 424937 280905 36080 1032 10000000 Resources 0,88 3,73 9,16 Statementsusage of OWLDB than2,33 for OWLIM, since10,6 (due to the persis- 24,92 OWLDB 600 4119 36427 738 4140271 1018 6239 tent on-disk storage in database tables) loading of ontologies occurs just once. In OWLIM, on the contrary, ontologies are Figure 6: Calculation of the subsumption relation loaded into main memory each time the system is started. for various ontologies (Note the logarithmic scale). 800.00 OWLDB computes the subsumption relation significantly faster for 4 out of the 7 ontologies. Pellet’s and OWLDB’s 600.00 performance are comparable for the two small ontologies OBO Pathway and SUMO. For the Galen ontology OWLDB 400.00 is significantly slower. Profiling OWLDB for Galen showed that 90% of the computation was spend on computing the 200.00 transitive closure of the subsumption relation (rule 1) and on the detection of intersection classes where each member 0.00 Sesame OWLDB Sesame OWLDB Sesame OWLDB is a super-class of a member of a second intersection class DL1 DL1 DL5 DL5 DL10 DL10 (rule 69). The former is very probable due to the - with 10 Inferencing 84.00 220.00 678.00 - high average depth of the class tree, the latter due to the Loading 3.78 16.93 37.78 large number of intersection classes (2024). Parsing 7.16 28.60 55.22 Pars.+Load.+Inf. 24.00 119.00 276 5.4 Comparison with Triple Stores To evaluate OWLDB’s ABox reasoning and querying per- Figure 7: Loading of UOB ontologies into OWLIM formance, we used the University Ontology Benchmark for and OWLDB. For OWLDB numbers are broken down into OWL DL (UOB [21]) of the UOB ontology with instance inferencing, loading and parsing. data for 1, 5, and 10 universities (later referred to as UOB- DLx). Sesame [10] (version 1.2.6) together with its OWLIM storage and inference layer [18] (version 2.8.4) served as a 5.4.2 Querying reference system for performance comparison. OWLDB is capable to answer all UOB queries sound and Storing ontologies in relational databases gives developers complete. OWLIM has problems answering the following more flexibility to fine-tune table layouts and index struc- UOB queries : tures in order to facilitate reasoning, inferencing, and query- • No results are returned for: ing in specific scenarios. For this evaluation, OWLDB was Version Query Reference configured to store inferred facts together with explicit in- UOB-DL5 5 200 formation from the UOB ontologies in the statements ta- UOB-DL5 9 1041 ble additionally in separate property tables (cf. [35] for UOB-DL5 14 6913 a discussion about property tables). This facilitates high- performance querying, but it may, however, result in slightly • An incomplete result set is returned for: longer load and update times. Version Query OWLIMs Reference UOB-DL1 14 6643 6893 5.4.1 Loading UOB-DL5 11 6210 6230 We first compared the load times (see Figure 7). OWLDB UOB-DL5 14 6696 6913 is roughly 3 times slower than OWLIM when parsing the UOB-DL10 14 6712 7088 RDF files, load them into the data structures and perform ABox inferences. We identified the following reasons: • The answers for query 15 are not sound: OWLIM returns 379 (416, 408) results instead of 62 • Parsing of RDF and loading into the data structures (76, 79) for DL1 (DL5, DL10). 10000 eLUMB DL1 6. RELATED WORK 1000 Traditionally, approaches for reasoning and inferencing for Description Logics are either optimized for TBox reasoning 100
Time (ms) in form of tableau based description logic reasoners or im- 10 plemented as proprietary or database backed instance stores with ABox reasoning capabilities. In addition there exist ef- 1 123456789101112131415 forts to integrate both strategies as-is into larger systems. Sesame 82 9 75 1553 11 107 98 42 18 1 2883 267 43 118 46 The problem of scalability is furthermore tackled by ap- ODB 34 100 35 17 5 5 1 10 86 3 270 5 10 244 9 proaches to modularize ontologies. Other approaches and 10000 eLUMB DL5 developments in addition to the ones presented in this sec- 1000 tion can be found in the slightly outdated SWAD deliver- able [7]. 100 Time (ms) 10 6.1 Description Logic Reasoners One of the few native OWL reasoners is Pellet [32] — 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 an open-source OWL-DL reasoner written in Java. Pellet Sesame 155 18 160 3089 3 159 188 82 34 1 23582 614 121 257 120 ODB 2 333 33 17 6 28 7 10 98 3 971 12 12 414 13 is based on tableau algorithms developed for expressive de-
10000 scription logics. It supports full OWL-DL including reason- eLUMB DL10 ing about nominals. Pellet is becoming increasingly popular 1000 due to its easy deployment and the ability to directly load any OWL ontology. RACER [13] is a very well optimized 100 and maybe the fastest tableau-based reasoner. However, Time (ms) 10 both Pellet and RACER perform in-memory reasoning and are due to the memory requirements of tableau reasoning 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 limited with regard to scalability and do not offer to selec- Sesame 303 35 362 7153 4 351 407 170 86 1 1E+0 1084 220 456 223 tively disable computationally expensive reasoning steps in ODB 1 656 54 18 6 61 2 10 115 3 1185 7 14 438 13 order to trade completeness for speed as OWLDB does. A system which apparently has many similarities to the pre- Figure 8: OWLDB and OWLIM querying perfor- sented approach is KAON2 [23]. It realizes on-disk reason- mance results for the University Ontology Bench- ing for a subset of OWL with disjunctive datalog, which is mark with instance data for 1, 5 and 10 universities. close to other database query languages such as SQL. Due to KAON2’s missing support for nominals we were not able to compare both systems directly. Table 8 summarizes OWLDB’s and OWLIM’s query per- formance. Please note the logarithmic scale. OWLDB is 6.2 Instance Stores able to answer 10 out of 15 UOB queries significantly (2 to Instance stores such as Jena [36], Sesame [10], OWLIM [18], over 100 times) faster than OWLIM. OWLIM outperforms Mulgara1 and AllegroGraph2 mainly focus on the efficient OWLDB in 4 queries (i.e. 2, 5, 9, 10) by approximately 2 to processing of ABox queries and support rule-based TBox in- 15 times. In addition, OWLDB is capable to support OWL ferences often only in a very limited way. The Jena toolkit features not included in the University Ontology Benchmark for example implements a Java API including support for (e.g. more complex subsumption reasoning). different database backends and light-weight forward- and backward-chaining RDF-Schema reasoning together with sup- 5.5 Profiling OWLDB reasoning port for the declarative RDF query languages RDQL and In order to gain insights which OWL expressions are the SPARQL. A system primarily focused on efficient parsing, most expensive ones with respect to reasoning in OWLDB, storing and querying is Sesame. In addition to accessing re- we profiled the timings of SQL query execution for each of lational databases for storing RDF data, Sesame provides a the evaluation ontologies. Surprisingly, more than 50% of highly optimized in-memory RDF storage layer, known to the overall query execution time was caused by only two be very fast in computing and materializing entailed state- query types: ments. Its modular structure allows the implementation of customized Storage and Inference Layers (SAIL). The • reasoning and inferences involving transitive proper- reference system of our evaluation OWLIM for example is ties with large property extents (including the RDF-S such a Sesame SAIL. OWLIM though aims at balancing be- and OWL vocabulary properties, owl:sameAs, rdfs: tween a scalable repository and light-weight reasoner and subClassOf) in-memory, forward chaining rule inferences based on De- scription Logic Programs. • subsumption inferences on the basis of the inference rule 69 (i.e. the detection of intersection classes where 6.3 Combined Approaches each member is a super-class of a member of a second One of the earliest approaches to coupling a DL reasoner intersection class). with a database is described in [8]. It uses SQL to clas- sify instances stored in a database and loading them into Hence, further significant performance improvements can be expected from optimizing these queries either at the database 91http://www.mulgara.org or application level. 92http://www.franz.com/products/allegrograph the CLASSIC system. In the context of the Semantic Web, problem, we would also like to explore how data integration the DLDB [26] system was an early approach to use an techniques [20, 14], which provide view-based data trans- RDBMS for RDF and limited RDF-S entailment and con- lation capabilities, might be extended to incorporate OWL necting it with a reasoner for DAML+OIL subsumption. reasoning capabilities in a similar way to OWLDB. Such an More recently, InstanceStore [6] and Minerva [38] combined architecture would provide an excellent basis for semantic a tableau based DL reasoner for the TBox inference with data sharing across ontologies when the classes do not pre- rules for the ABox inference. In Minerva rules are trans- cisely align: for instance, database schema mappings can lated into SQL queries on a relational triple store schema. convert between prices in different currencies, or from one However, the selected rule language in Minerva is relatively type of local ID to another. weak and focuses mainly on instance retrieval. 6.4 Modularization of Ontologies 8. ACKNOWLEDGMENTS Another way to cope with the growing size of ontolo- We would like to thank Joe Kopena, Frank Loebe, Jens gies in addition to more efficient indexing and better op- Lehmann and Robert Hoehndorf for fruitful discussions and timized algorithms is to segment ontologies into reasonably valuable suggestions. self-contained parts for separate processing. Work with re- gard to the modularization of ontologies can be categorized 9. REFERENCES along three main categories: [1] S. Auer. Powl: A web based platform for collaborative • Query-based methods aiming at generating views of on- semantic web development. In S. Auer, C. Bizer, and tologies by means of database inspired query languages L. Miller, editors, Proceedings of the Workshop such as SPARQL [27], Scripting for the Semantic Web, number 135 in CEUR Workshop Proceedings, Heraklion, Greece, 05 2005. • Network partitioning, which views ontologies as net- [2] S. Auer, S. Dietzold, and T. Riechert. 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