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Forgetting and Uniform Interpolation in LargeScale Description Logic Terminologies
"... We develop a framework for forgetting concepts and roles (aka uniform interpolation) in terminologies in the lightweight description logic EL extended with role inclusions and domain and range restrictions. Three different notions of forgetting, preserving, respectively, concept inclusions, concept ..."
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Cited by 28 (4 self)
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We develop a framework for forgetting concepts and roles (aka uniform interpolation) in terminologies in the lightweight description logic EL extended with role inclusions and domain and range restrictions. Three different notions of forgetting, preserving, respectively, concept inclusions, concept instances, and answers to conjunctive queries, with corresponding languages for uniform interpolants are investigated. Experiments based on SNOMED CT (Systematised Nomenclature of
Logicbased ontology comparison and module extraction, with an application to DLLite
 ARTIFICIAL INTELLIGENCE
, 2010
"... We develop a formal framework for comparing different versions of DLLite ontologies. The main feature of our approach is that we take into account the vocabulary ( = signature) with respect to which one wants to compare ontologies. Five variants of difference and inseparability relations between on ..."
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Cited by 13 (6 self)
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We develop a formal framework for comparing different versions of DLLite ontologies. The main feature of our approach is that we take into account the vocabulary ( = signature) with respect to which one wants to compare ontologies. Five variants of difference and inseparability relations between ontologies are introduced and their respective applications for ontology development and maintenance discussed. These variants are obtained by generalising the notion of conservative extension from mathematical logic and by distinguishing between differences that can be observed among concept inclusions, answers to queries over ABoxes, by taking into account additional context ontologies, and by considering a modeltheoretic, languageindependent notion of difference. We compare these variants, study their metaproperties, determine the computational complexity of the corresponding reasoning tasks, and present decision algorithms. Moreover, we show that checking inseparability can be automated by means of encoding into QBF satisfiability and using offtheshelf general purpose QBF solvers. Inseparability relations between ontologies are then used to develop a formal framework for (minimal) module extraction. We demonstrate that different types of minimal modules induced by these inseparability relations can be automatically extracted from realworld mediumsize DLLite ontologies by composing the tractable syntactic localitybased module extraction algorithm with nontractable extraction algorithms using the multiengine QBF solver aqme. Finally, we explore the relationship between uniform interpolation (or forgetting) and inseparability between ontologies.
Concept and Role Forgetting in ALC Ontologies
, 2009
"... Abstract. Forgetting is an important tool for reducing ontologies by eliminating some concepts and roles while preserving sound and complete reasoning. Attempts have previously been made to address the problem of forgetting in relatively simple description logics (DLs) such as DLLite and extended E ..."
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Cited by 8 (1 self)
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Abstract. Forgetting is an important tool for reducing ontologies by eliminating some concepts and roles while preserving sound and complete reasoning. Attempts have previously been made to address the problem of forgetting in relatively simple description logics (DLs) such as DLLite and extended EL. The ontologies used in these attempts were mostly restricted to TBoxes rather than general knowledge bases (KBs). However, the issue of forgetting for general KBs in more expressive description logics, such as ALC and OWL DL, is largely unexplored. In particular, the problem of characterizing and computing forgetting for such logics is still open. In this paper, we first define semantic forgetting about concepts and roles in ALC ontologies and state several important properties of forgetting in this setting. We then define the result of forgetting for concept descriptions in ALC, state the properties of forgetting for concept descriptions, and present algorithms for computing the result of forgetting for concept descriptions. Unlike the case of DLLite, the result of forgetting for an ALC ontology does not exist in general, even for the special case of concept forgetting. This makes the problem of how to compute forgetting in ALC more challenging. We address this problem by defining a series of approximations to the result of forgetting for ALC ontologies and studying their properties and their application to reasoning tasks. We use the algorithms for computing forgetting for concept descriptions to compute these approximations. Our algorithms for computing approximations can be embedded into an ontology editor to enhance its ability to manage and reason in (large) ontologies. 1
Tableaubased Forgetting in ALC Ontologies
"... Abstract. In this paper, we propose two new and different approaches to forgetting variables for ALC based on the wellknown tableau algorithm. The first approach computes the result of forgetting via rolling up tableaux, which also provides insights of the decidability of existence of forgetting in ..."
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Abstract. In this paper, we propose two new and different approaches to forgetting variables for ALC based on the wellknown tableau algorithm. The first approach computes the result of forgetting via rolling up tableaux, which also provides insights of the decidability of existence of forgetting in ALC. When the result of forgetting does not exist, we provide an incremental method for computing approximations of forgetting. The second approach uses variable substitution to refine approximations of forgetting and eventually obtain the result of forgetting. This approach is capable of preserving structural information of the original ontologies and thus renders readability. As both approaches are based on the tableau algorithm, their implementations can make use of the mechanisms and optimization techniques of the existing description logic reasoners. 1
Functional stable model semantics and answer set programming modulo theories
 In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR
, 2012
"... ”Answer Set Programming Modulo Theories (ASPMT) ” is a recently proposed framework which tightly integrates answer set programming (ASP) and satisfiability modulo theories (SMT). Its mathematical foundation is the functional stable model semantics, an enhancement of the traditional stable model sema ..."
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Cited by 5 (5 self)
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”Answer Set Programming Modulo Theories (ASPMT) ” is a recently proposed framework which tightly integrates answer set programming (ASP) and satisfiability modulo theories (SMT). Its mathematical foundation is the functional stable model semantics, an enhancement of the traditional stable model semantics to allow defaults involving functions as well as predicates. This talk will discuss how ASPMT can provide a way to overcome limitations of the propositional setting of ASP, how action language C+ can be reformulated in terms of ASPMT, and how it can be 3 4 Answer Set Programming (ASP) Declarative programming paradigm. Suitable for knowledge intensive
Towards Closed World Reasoning in Dynamic Open Worlds
 TPLP Special Issue 10(46
, 2010
"... The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases composed of both an ontology (expressed in a fragment ..."
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Cited by 5 (4 self)
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The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases composed of both an ontology (expressed in a fragment of firstorder logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve. In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties. To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.
Forgetting and uniform interpolation in extensions of the description logic
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Forgetting for Knowledge Bases in DLLite
"... To support the reuse and combination of ontologies in Semantic Web applications, it is often necessary to obtain smaller ontologies from existing larger ontologies. In particular, applications may require the omission of certain terms, e. g., concept names and role names, from an ontology. However, ..."
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Cited by 3 (1 self)
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To support the reuse and combination of ontologies in Semantic Web applications, it is often necessary to obtain smaller ontologies from existing larger ontologies. In particular, applications may require the omission of certain terms, e. g., concept names and role names, from an ontology. However, the task of omitting terms from an ontology is challenging because the omission of some terms may affect the relationships between the remaining terms in complex ways. We present the first solution to the problem of omitting concepts and roles from knowledge bases of description logics (DLs) by adapting the technique of forgetting, previously used in other domains. Specifically, we first introduce a modeltheoretic definition of forgetting for knowledge bases (both TBoxes and ABoxes) in DLLite N bool, which is a nontrivial adaption of the standard definition for classical logic, and show that our modelbased forgetting satisfies all major criteria of a rational forgetting operator, which in turn verifies the suitability of our modelbased forgetting. We then introduce algorithms that implement forgetting operations in DLLite knowledge bases. We prove that the algorithms are correct with respect to the semantic definition of forgetting. We establish a general framework for defining and comparing different definitions of forgetting by introducing a parameterized family of forgetting operators called querybased forgetting operators. In this framework we identify three specific querybased forgetting operators and show that they form a hierarchy. In particular, we show that the modelbased forgetting coincides with one of these querybased forgetting operators.
Mathematical logic for life science ontologies
 DE QUEIROZ (EDS.), LOGIC, LANGUAGE, INFORMATION AND COMPUTATION, 16TH INT. WORKSHOP, WOLLIC 2009
, 2009
"... We discuss how concepts and methods introduced in mathematical logic can be used to support the engineering and deployment of life science ontologies. The required applications of mathematical logic are not straighforward and we argue that such ontologies provide a new and rich family of logical th ..."
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Cited by 2 (2 self)
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We discuss how concepts and methods introduced in mathematical logic can be used to support the engineering and deployment of life science ontologies. The required applications of mathematical logic are not straighforward and we argue that such ontologies provide a new and rich family of logical theories that wait to be explored by logicians.
Uniform Interpolation for ALC Revisited
"... The notion of uniform interpolation for description logic ALC has been ..."
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The notion of uniform interpolation for description logic ALC has been