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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 45 (6 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 24 (8 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 13 (3 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
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 11 (3 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.
A Modeltheoretic Approach to Belief Change in Answer Set Programming
"... We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Our formal techniques are analogous to those of distancebased belief revision in propositional logic. In particular, we build upon the model theory of logic programs furnished by SE interpretatio ..."
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Cited by 7 (1 self)
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We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Our formal techniques are analogous to those of distancebased belief revision in propositional logic. In particular, we build upon the model theory of logic programs furnished by SE interpretations, where an SE interpretation is a model of a logic program in the same way that a classical interpretation is a model of a propositional formula. Hence we extend techniques from the area of belief revision based on distance between models to belief change in logic programs. We first consider belief revision: for logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P ∗ Q. We investigate several operators, including (logic program) expansion and two revision operators based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical belief revision where it is relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy all or nearly all of the AGM postulates for revision. We next consider approaches for merging a set of logic programs, P1,..., Pn. Again, our formal techniques are based on notions of relative distance between the SE models of the logic programs. Two approaches
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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Cited by 6 (0 self)
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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
Forgetting and uniform interpolation in extensions of the description logic
"... EL ..."
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Forgetting for Defeasible Logic
"... Abstract. The concept of forgetting has received significant interest in artificial intelligence recently. Informally, given a knowledge base, we may wish to forget about (or discard) some redundant parts (such as atoms, predicates, concepts, etc) but still preserve the consequences for certain form ..."
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Cited by 6 (4 self)
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Abstract. The concept of forgetting has received significant interest in artificial intelligence recently. Informally, given a knowledge base, we may wish to forget about (or discard) some redundant parts (such as atoms, predicates, concepts, etc) but still preserve the consequences for certain forms of reasoning. In nonmonotonic reasoning, so far forgetting has been studied only in the context of extension based approaches, mainly answerset programming. In this paper forgetting is studied in the context of defeasible logic, which is a simple, efficient and sceptical nonmonotonic reasoning approach. 1
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 6 (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.
Interpolable Formulas in Equilibrium Logic and Answer Set Programming
"... Interpolation is an important property of classical and many nonclassical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the nonmonotonic system of equilibrium logic, establishing weaker or stronger forms of ..."
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Cited by 4 (1 self)
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Interpolation is an important property of classical and many nonclassical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the nonmonotonic system of equilibrium logic, establishing weaker or stronger forms of interpolation depending on the precise interpretation of the inference relation. These results also yield a form of interpolation for ground logic programs under the answer sets semantics. For disjunctive logic programs we also study the property of uniform interpolation that is closely related to the concept of variable forgetting. The firstorder version of equilibrium logic has analogous Interpolation properties whenever the collection of equilibrium models is (firstorder) definable. Since this is the case for socalled safe programs and theories, it applies to the usual situations that arise in practical answer set programming. 1.