DRAOn is a distributed reasoner which offers inference services for a network of OWL ontologies correlated by alignments. Reasoning with such networks of ontologies depends on the semantics we define for alignments with respect to ontologies. DRAOn supports two semantics for a network of ontologies: the standard Description Logics (DL) semantics for non-distributed reasoning, and the Integrated Distributed Description Logics (IDDL) semantics for distributed reasoning. Unlike the DL semantics where alignments are considered as inter-ontology axioms, the IDDL semantics interprets alignments as correspondences enabling to propagate non-emptiness (always satisfiable) and unsatisfiability of atomic concepts from an ontology to another one. Consequently, this makes distributed reasoning for a network of ontologies possible since consistency of the whole network can be decided from consistency of each ontology with axioms built from alignments such that these axioms ensure just necessary propagations of knowledge.
We present DRAOn, a reasoner for a distributed network of aligned ontologies. The goal of DRAOn is to be able to reason on a set of independently developed ontologies that may overlap in concepts but are following different modelling perspectives, granularity, coverage, etc. To be able to do that, we assume that there exists explicit correspondences between different ontologies, that have been built by automatic ontology matchers, by humans, or partly by both. Therefore, the structure that DRAOn is reasoning with is not a monolithical theory, but a network of aligned ontologies. Moreover, DRAOn is able to make use of existing reasoners as black boxes for some of its tasks.
The issues faced when reasoning with heterogeneous, distributed ontologies, even when they have been already matched, are twofold: (a) the semantics of cross-ontology correspondences can be tricky to define when ontologies have different modelling perspectives because a correspondence of terms from different ontologies does not necessarily translates directly to an axiom in the ontology language (or languages); and (b) the distribution of ontologies, and possibly of reasoning services associated with them may influence the design of the global reasoner.
In this paper, we assume that ontologies are all Description Logic theories and we
assume some familiarity with DLs. We simply repeat that DL ontologies are interpreted
according to an interpretation function I over a domain I , and interpretations that
satisfy all the axioms of an ontology are called models of the ontology. There are a
number of existing OWL DL reasoners such as HermiT [
In order to use several ontologies for reasoning, we assume the existence of correspondences between ontologies of the form (ei; ej ; r), where ei is a term from one ontology, ej a term from another ontology, and r denotes a fixed binary relation such as equality, subsumption, disjointness, etc. In this paper, only correspondences where r is = (equality of individuals), 2 (class membership) or v (subsumption) will be considered. A set of correspondences between a pair of ontologies is an ontology alignment (or alignment for short). A set of ontologies together with their pairwise alignments is called a network of aligned ontologies (NAO). We will use bold face to denote sets, and therefore, the notation for an NAO will generally be hO; Ai.
Reasoning with NAOs strongly depends on the semantics of alignments. We say that a certain semantics of alignments defines a distributed logic (sometimes called “contextual logic“ or even “modular ontology language”). In a distributed logic L, correspondences map to formula of the logic in question, so we will use a function L to denote the logical formula associated to the correspondence. For instance, the simplest form of distributed logic is normal DL. An NAO can be interpreted as a DL ontology by mapping (ei; ej ; v) (resp. (ei; ej ; =), (ei; ej ; 2)) to DL(ei; ej ; v) = ei v ej (resp. ei = ej , ej (ei)). Reasoning over an NAO is then the same as reasoning with an ontology formed by the union of all the ontologies in the NAO, and the axioms corresponding to the correspondences.
A number of authors, including ourselves, have argued that this is not satisfying
when dealing with heterogeneous ontologies. Therefore, several other distributed
logics were proposed. Here we focus on the ones that are adopting a Local Model
Semantics (LMS [
As opposed to E -connections and DDL, which treats correspondences as subjective views of an ontology wrt another ontology’s terms, we proposed Integrated Distributed Description Logics (IDDL) as a distributed logic that assumes local ontologies are agnostic to each others, and correspondences express knowledge of a mediation view that ties together the ontologies. In IDDL, DDL(ei; ej ; v) = i:ei v! j:ej is simply called a correspondence. An IDDL interpretation of an NAO hO; Ai is a structure hI; i such that I = fIogo2O is a set of DL interpretations of the ontologies, and = f o : Io ! go2O is a set of functions (so called equalising functions) from local domains of interpretations to a set called the global domain. The composition of a local interpretation function Ii with its corresponding equalising function i defines the global interpretations of local terms. A correspondence i:ei v! j:ej is satisfied iff i(eiIi ) j (ejIj ).4
There are implementations of DDL (Drago, a tableau-based peer-to-peer reasoner [
DRAOn implements the algorithm in [
Let hO; Ai be an NAO where O is a set of DL decidable ontologies, and A is a set of alignments between these ontologies. We assume that each ontology o 2 O is attached to a reasoner that can be queried with a set X of DL axioms and answer whether o [ X is consistent. Then, checking the consistency of an NAO amounts to querying the local reasoners multiple times with a well chosen set of axioms. The main idea is that, when correspondences are restricted to cross-ontology subsumption, equality or membership, alignments can only influence the vacuity (unsatisfiability) and non-vacuity (non-emptiness) of concepts or roles appearing in the alignments.
The main steps of the algorithm are the following: 1. build an alignment ontology, noted A, which corresponds to the translation of correspondences into OWL axioms (using DL mentioned in Sect. 2); 2. if A is inconsistent then the NAO is inconsistent; 3. choose a subset S (resp. P ) of the concepts (resp. roles) appearing in A to build a global configuration consisting of axioms Ci(x) (non-emptiness) with x a fresh individual name for each Ci 2 S and Cj v ? (unsatisfiability) for each Cj 62 S (resp., Ri(x; y) for R 2 P and > v 8Rj :? instead); 4. for a given ontology o, define a local configuration wrt o as the subset of which involves only terms from o, noted !o; 5. if A [ is inconsistent, then go back to step 3; 6. for each o 2 O, query the local reasoner attached to o using the axioms in !o; if all local reasoners answer positively, then the network is consistent. Otherwise, go back to step 3 until there are no more configuration available. 4 For a set S, (S) has to be understood as the set f (x) j x 2 Sg. 3.2
In terms of system architecture, DRAOn consists of a global OWL reasoner and several local OWL reasoners. The global reasoner is in charge of (i) computing global configurations , (ii) checking consistency of A [ for each global configuration and (iii) sending a local configuration to each local reasoner. Each local reasoner checks consistency of o [ .
The distributed behavior of the algorithm results from a feature of IDDL which does not enforce a strong relationship between alignments and ontologies. Instead of merging ontologies and alignments into a unique ontology, DRAOn distributes reasoning tasks over ontologies to different local reasoners. In addition to early improvements, we implement optimizations for reducing the number of configurations to be considered and for improving communication protocol between global and local reasoners. The main ideas are: – Global configurations are built in an incremental way, and results obtained from checking previous configurations are reused. For each configuration, we check entailment rather than consistency. This allows for putting forward eventual backtracking points. For example, if Oi j= Ci v ? (resp. Oi j= Ci(x)) then we do not need to check the configurations that contain Oi j= Ci(x) (resp. Ci v ?). – If there is a set of concepts (or roles) which are equivalent, we need to check only configurations which contain one representative concept (or role) from this set. – Configurations consisting of non-emptiness axioms Ci(x) are checked prior to those consisting of unsatisfiability axioms Cj v ?. This idea is based on the fact that concepts are commonly satisfiable in ontologies. – The communication protocol between global and local reasoners is parallelized, that means, configurations are sent to local reasoners in a broadcasting way rather than a sequential one. The global reasoner uses Java threads to manage communication with the local reasoners. We have to use sockets to establish the communication between global and local reasoners instead of OWLLink5. This is due to efficiency question and an intrinsic characteristic of IDDL.
Apart from checking consistency of an NAO, the current version of DRAOn implements entailment services under the IDDL semantics for some kinds of entailment concept axioms. Therefore, DRAOn offers the following inference services: – Checking consistency of an NAO under the DL semantics in a non-distributed way.
In this setting, DRAOn creates a unique OWL ontology, namely global ontology, that is obtained by merging the axioms of all ontologies and the correspondences of alignments. Reasoning on the global ontology is performed in a non-distributed way, that means, a OWL reasoner is used for checking consistency of the global ontology. The network is consistent if and only if the global ontology is consistent – Checking entailment of an OWL axiom by an NAO under the DL semantics in a non-distributed way; 5 http://www.owllink.org/ – Checking consistency of an NAO based on the IDDL semantics in a non-distributed way, that is, all reasoning over ontologies and alignments is sequentially performed at one site on a computer. – Checking consistency of an NAO based on the IDDL semantics in a distributed way. – Checking entailment of some kinds of OWL axioms by a network of aligned ontologies based on the IDDL semantics in a distributed way. 4
DRAOn uses the OWL API6 to manipulate ontologies, the Alignment API [
Ontology 1 Ontology 2 Alignment DL non-distr. IDDL distr. IDDL Small NCI Small FMA Alcomo Map. 7,5s 46s 30s (10,000 axioms, (3,800 axioms, (2,800 corr.) 6,500 entities) 3,700 entities)
Human Mouse Ref. Map. 6s 4.5s 4s (5,500 axioms, ( 4,500 axioms, (1516 corr.) 3,300 entities) 2,750 entities) IDDL reasoning performances depend on the two services OWLReasoner.getTypes(.) and OWLReasoner.getUnsatisfiableClasses() which are called for checking unsatisfiability and non-emptiness of concepts involved in alignments. These services check for unsatisfiability and non-emptiness every concept name occurring in an ontology while the algorithm for IDDL consistency requires to check for unsatisfiability and non-emptiness only concepts involved in alignments. Consequently, HermiT raises an “OutOfMemoryError ” when it is called for getTypes(.) on the ontology “Small SNOMED”.
Theoretically, response time of inference services under the DL and IDDL semantics increases, respectively, double exponentially and exponentially in the number of ontologies (and the size of alignments). To make this difference occur, we might need a very large network of aligned ontologies. In addition, it might be required to perform further experiments to establish relationships between kinds of aligned ontologies and IDDL reasoning performance. 6 http://owlapi.sourceforge.net/ 7 http://www.hermit-reasoner.com/ 8 http://iddl.gforge.inria.fr/
We have presented an OWL-based distributed reasoner, called DRAOn, which offers inference services for a network of aligned OWL ontologies. The distributed behavior of DRAOn is based on a feature of the IDDL semantics which allows a reasoner to distribute reasoning tasks over ontologies to different reasoners. In terms of performance, DRAOn is considerably penalized by unavailability of specific services of an OWL reasoner, for instance, returning all unsatisfiable concepts which belong to a given set of concepts; or returning all non-empty concepts which belong to a given set of concepts. Availability of such services in a future release of OWL reasoners may improve dramatically the performance of DRAOn.
We intend to extend DRAOn to reasoning on a network with disjointness correspondences in alignments. This may require us to develop new optimizations since the current algorithm for such a network is highly intractable.