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Modelbased Revision Operators for Terminologies in Description Logics
"... The problem of revising an ontology consistently is closely related to the problem of belief revision which has been widely discussed in the literature. Some syntaxbased belief revision operators have been adapted to revise ontologies in Description Logics (DLs). However, these operators remove the ..."
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The problem of revising an ontology consistently is closely related to the problem of belief revision which has been widely discussed in the literature. Some syntaxbased belief revision operators have been adapted to revise ontologies in Description Logics (DLs). However, these operators remove the whole axioms to resolve logical contradictions and thus are not finegrained. In this paper, we propose three modelbased revision operators to revise terminologies in DLs. We show that one of them is more rational than others by comparing their logical properties. Therefore, we focus on this revision operator. We also consider the problem of computing the result of revision by our operator with the help of the notion of concept forgetting. Finally, we analyze the computational complexity of our revision operator. 1
Decomposing description logic ontologies
, 2010
"... Recent years have seen the advent of large and complex ontologies, most notably in the medical domain. As a consequence, structuring mechanisms for ontologies are nowadays viewed as an indispensible tool. A basic such mechanism is the automatic decomposition of the vocabulary of an ontology into ind ..."
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Recent years have seen the advent of large and complex ontologies, most notably in the medical domain. As a consequence, structuring mechanisms for ontologies are nowadays viewed as an indispensible tool. A basic such mechanism is the automatic decomposition of the vocabulary of an ontology into independent parts. In this paper, we study decompositions that are syntax independent in the sense that the resulting partitioning depends only on the meaning of the vocabulary items, but not on the concrete syntactic form of the axioms in the ontology. We present the first systematic investigation of decompositions of this type in the context of ontologies. Specifically, we focus on ontologies formulated in description logics and provide a variety of results that range from theorems stating the existence of unique finest decompositions to complexity results and algorithms computing decompositions. We also investigate the relationship between the existence of unique finite decompositions and a variant of the Craig interpolation property called parallel interpolation.
The logical difference for the lightweight description logic EL
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESERACH (JAIR
, 2012
"... We study a logicbased approach to versioning of ontologies. Under this view, ontologies provide answers to queries about some vocabulary of interest. The difference between two versions of an ontology is given by the set of queries that receive different answers. We investigate this approach for te ..."
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Cited by 13 (8 self)
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We study a logicbased approach to versioning of ontologies. Under this view, ontologies provide answers to queries about some vocabulary of interest. The difference between two versions of an ontology is given by the set of queries that receive different answers. We investigate this approach for terminologies given in the description logic EL extended with role inclusions and domain and range restrictions for three distinct types of queries: subsumption, instance, and conjunctive queries. In all three cases, we present polynomialtime algorithms that decide whether two terminologies give the same answers to queries over a given vocabulary and compute a succinct representation of the difference if it is nonempty. We present an implementation, CEX2, of the developed algorithms for subsumption and instance queries and apply it to distinct versions of Snomed CT and the NCI ontology.
Query and Predicate Emptiness in Description Logics
, 2010
"... Ontologies can be used to provide an enriched vocabulary for the formulation of queries over instance data. We identify query emptiness and predicate emptiness as two central reasoning services in this context. Query emptiness asks whether a given query has an empty answer over all data sets formula ..."
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Cited by 13 (6 self)
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Ontologies can be used to provide an enriched vocabulary for the formulation of queries over instance data. We identify query emptiness and predicate emptiness as two central reasoning services in this context. Query emptiness asks whether a given query has an empty answer over all data sets formulated in a given signature. Predicate emptiness is defined analogously, but quantifies universally over all queries that contain a given predicate. In this paper, we determine the computational complexity of query emptiness and predicate emptiness in the EL, DLLite, and ALCfamilies of description logics, investigate the connection to ontology modules, and perform a practical case study to evaluate the new reasoning services.
Beth Definability in Expressive Description Logics
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... The Beth definability property, a wellknown property from classical logic, is investigated in the context of description logics (DLs): if a general LTBox implicitly defines an Lconcept in terms of a given signature, where L is a DL, then does there always exist over this signature an explicit def ..."
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The Beth definability property, a wellknown property from classical logic, is investigated in the context of description logics (DLs): if a general LTBox implicitly defines an Lconcept in terms of a given signature, where L is a DL, then does there always exist over this signature an explicit definition in L for the concept? This property has been studied before and used to optimize reasoning in DLs. In this paper a complete classification of Beth definability is provided for extensions of the basic DL ALC with transitive roles, inverse roles, role hierarchies, and/or functionality restrictions, both on arbitrary and on finite structures. Moreover, we present a tableaubased algorithm which computes explicit definitions of at most double exponential size. This algorithm is optimal because it is also shown that the smallest explicit definition of an implicitly defined concept may be double exponentially long in the size of the input TBox. Finally, if explicit definitions are allowed to be expressed in firstorder logic then we show how to compute them in EXPTIME.
Semantics of the Distributed Ontology Language: Institutes and Institutions
"... The Distributed Ontology Language (DOL) is a recent development within the ISO standardisation initiative 17347 Ontology Integration and Interoperability (OntoIOp). In DOL, heterogeneous and distributed ontologies can be expressed, i.e. ontologies that are made up of parts written in ontology lang ..."
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Cited by 2 (2 self)
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The Distributed Ontology Language (DOL) is a recent development within the ISO standardisation initiative 17347 Ontology Integration and Interoperability (OntoIOp). In DOL, heterogeneous and distributed ontologies can be expressed, i.e. ontologies that are made up of parts written in ontology languages based on various logics. In order to make the DOL metalanguage and its semantics more easily accessible to the wider ontology community, we have developed a notion of institute which are like institutions but with signature partial orders and based on standard settheoretic semantics rather than category theory. We give an institutebased semantics for the kernel of DOL and show that this is compatible with institutional semantics. Moreover, as it turns out, beyond their greater simplicity, institutes have some further surprising advantages over institutions.
Module Extraction for Acyclic Ontologies
"... Abstract. We present an implementation (AMEX) of a module extraction algorithm for acyclic description logic ontologies. The implementation uses a QBF solver (sKizzo) to check whether one ontology is a conservative extension of another ontology relativised to interpretations of cardinality one. We e ..."
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Abstract. We present an implementation (AMEX) of a module extraction algorithm for acyclic description logic ontologies. The implementation uses a QBF solver (sKizzo) to check whether one ontology is a conservative extension of another ontology relativised to interpretations of cardinality one. We evaluate AMEX by applying it to NCI (the National Cancer Institute Thesaurus) and by comparing the extracted AMEXmodules with localitybased modules. We also present experiments for a hybrid approach in which AMEX and localitybased module extraction are applied iteratively to NCI. 1
Lower and Upper Approximations for Depleting Modules of Description Logic Ontologies
"... It is known that no algorithm can extract the minimal depleting Σmodule from ontologies in expressive description logics (DLs). Thus research has focused on algorithms that approximate minimal depleting modules ‘from above ’ by computing a depleting module that is not necessarily minimal. The firs ..."
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It is known that no algorithm can extract the minimal depleting Σmodule from ontologies in expressive description logics (DLs). Thus research has focused on algorithms that approximate minimal depleting modules ‘from above ’ by computing a depleting module that is not necessarily minimal. The first contribution of this paper is an implementation (AMEX) of such a depleting module extraction algorithm for expressive acyclic DL ontologies that uses a QBF solver for checking conservative extensions relativised to singleton interpretations. To evaluate AMEX and other module extraction algorithms we propose an algorithm approximating minimal depleting modules ‘from below ’ (which also uses a QBF solver). We present experiments based on NCI (the National Cancer Institute Thesaurus) that indicate that our lower approximation often coincides with (or is very close to) the upper approximation computed by AMEX, thus proving for the first time that an approximation algorithm for minimal depleting modules can be almost optimal on a large ontology in a nontractable DL. We use standard notation from logic and description logic (DL), details can be found in [1]. In a DL, concepts are constructed from countably infinite sets NC of concept
Preservation of Modules
"... Abstract. Within the Common Logic Ontology Repository (COLORE), relationships among ontologies such as the notions of faithful interpretability, logical synonymy, and reducibility have been used for ontology verification. Earlier work has shown how to use these relationships to find modules of the ..."
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Abstract. Within the Common Logic Ontology Repository (COLORE), relationships among ontologies such as the notions of faithful interpretability, logical synonymy, and reducibility have been used for ontology verification. Earlier work has shown how to use these relationships to find modules of theories, so a natural question is to determine how we can use the decomposition of one theory into modules to find the modules of another theory in the repository. In this paper, we examine a number of ontologies for which faithful interpretability and logical synonymy do not preserve their modules. Nevertheless, we identify a class of interpretations among theories which guarantees that the modules of a theory are preserved. We also show that the modules of reducible theories are preserved by logical synonymy.
Progression of Decomposed Situation Calculus Theories *
"... Abstract In many tasks related to reasoning about consequences of a logical theory, it is desirable to decompose the theory into a number of components with weaklyrelated or independent signatures. This facilitates reasoning when the signature of a query formula belongs to only one of the componen ..."
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Abstract In many tasks related to reasoning about consequences of a logical theory, it is desirable to decompose the theory into a number of components with weaklyrelated or independent signatures. This facilitates reasoning when the signature of a query formula belongs to only one of the components. However, an initial theory may be subject to change due to execution of actions affecting features mentioned in the theory. Having once computed a decomposition of a theory, one would like to know whether a decomposition has to be computed again for the theory obtained from taking into account the changes resulting from execution of an action. In the paper, we address this problem in the scope of the situation calculus, where change of an initial theory is related to the wellstudied notion of progression. Progression provides a form of forward reasoning; it relies on forgetting values of those features which are subject to change and computing new values for them. We prove new results about properties of decomposition components under forgetting and show when a decomposition can be preserved in progression of an initial theory.