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Computing Least Common Subsumers in Description Logics with Existential Restrictions
, 1999
"... Computing the least common subsumer (lcs) is an inference task that can be used to support the "bottomup " construction of knowledge bases for KR systems based on description logics. Previous work on how to compute the lcs has concentrated on description logics that allow for univ ..."
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Cited by 119 (29 self)
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Computing the least common subsumer (lcs) is an inference task that can be used to support the &quot;bottomup &quot; construction of knowledge bases for KR systems based on description logics. Previous work on how to compute the lcs has concentrated on description logics that allow for universal value restrictions, but not for existential restrictions. The main new contribution of this paper is the treatment of description logics with existential restrictions. Our approach for computing the lcs is based on an appropriate representation of concept descriptions by certain trees, and a characterization of subsumption by homomorphisms between these trees. The lcs operation then corresponds to the product operation on trees.
Least Common Subsumers and Most Specific Concepts in a Description Logic with Existential Restrictions and Terminological Cycles
, 2003
"... Computing least common subsumers (Ics) and most specific concepts (msc) are inference tasks that can support the bottomup construction of knowledge bases in description logics. In description logics with existential restrictions, the most specific concept need not exist if one restricts the attenti ..."
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Cited by 94 (18 self)
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Computing least common subsumers (Ics) and most specific concepts (msc) are inference tasks that can support the bottomup construction of knowledge bases in description logics. In description logics with existential restrictions, the most specific concept need not exist if one restricts the attention to concept descriptions or acyclic TBoxes. In this paper, we extend the notions les and msc to cyclic TBoxes. For the description logic EC (which allows for conjunctions, existential restrictions, and the topconcept), we show that the les and msc always exist and can be computed in polynomial time if we interpret cyclic definitions with greatest fixpoint semantics.
Rewriting concepts using terminologies
 Proceedings of the Seventh International Conference on Knowledge Representation and Reasoning (KR2000
, 2000
"... The problem of rewriting a concept given a terminology can informally be stated as follows: given a terminology T (i.e., a set of concept definitions) and a concept description C that does not contain concept names defined in T, can this description be rewritten into a "related better & ..."
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Cited by 45 (6 self)
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The problem of rewriting a concept given a terminology can informally be stated as follows: given a terminology T (i.e., a set of concept definitions) and a concept description C that does not contain concept names defined in T, can this description be rewritten into a &quot;related better &quot; description E by using (some of) the names defined in T? In this paper, we first introduce a general framework for the rewriting problem in description logics, and then concentrate on one specific instance of the framework, namely the minimal rewriting problem (where &quot;better &quot; means shorter, and &quot;related &quot; means equivalent). We investigate the complexity of the decision problem induced by the minimal rewriting problem for the languages FL 0, ALN, ALE, and ALC, and then introduce an algorithm for computing (minimal) rewritings for the language ALE. (In the full paper, a similar algorithm is also developed for ALN.) Finally, we sketch other interesting instances of the framework.
Description logics for the representation of aggregated objects.
, 2000
"... Abstract. Aggregated objects play an important role in many knowledge representation applications. For the adequate representation of aggregated objects, it is crucial to represent partwhole relations. We discuss properties of partwhole relations and extend the description logic ALC with means fo ..."
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Cited by 27 (4 self)
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Abstract. Aggregated objects play an important role in many knowledge representation applications. For the adequate representation of aggregated objects, it is crucial to represent partwhole relations. We discuss properties of partwhole relations and extend the description logic ALC with means for the adequate representation of partwhole relations and thus of aggregated objects. Motivation Description logics are a family of knowledge representation formalisms wellsuited for the representation of and reasoning about configurations In all these applications, aggregated objects play a central role, that is, objects that are composed of various parts, which again can be composite, etc. It is natural to describe an aggregated object by means of its parts and vice versa, to describe parts by means of the aggregate they belong to. For example, the following statements describe a control rod and a reactor core by means of their parts and wholes, where v is a subsumption (implication) relationship: Controlrod v Device u 9 partof :Reactorcore Reactorcore v Device u 9 haspart :Controlrod u 9 partof :Nuclearreactor Referring to wholes a part belongs to, we use the partwhole relation (written partof and abbreviated pwrelation). Vice versa, to refer to the parts of an object, we use the haspart relation, which is the inverse of the pwrelation, is written haspart, and abbreviated hprelation. It is commonly believed [1] that only a formalism with very high expressive power can represent pwrelations and aggregated objects adequately. In this paper, we argue in how far the high expressive power of the description logic S H I Qis crucial for the adequate representation of aggregated objects. Despite S H I Q 's high expressiveness, there is a practicable reasoning algorithm which decides inference problems such as satisfiability and subsumption of S H I Qconcepts w.r.t. to (possibly cyclic) terminological knowledge bases. Some properties of PartWhole Relations In contrast to, for example, the relation likes, the pwrelation has a variety of properties. For a complete collection of these proper1 LuFG Theoretical Computer Science, RWTH Aachen, Germany, email: sattler@cs.rwthaachen.de ties, we refer to SubRelations of the General PartWhole Relation Besides the properties mentioned above, the pwrelation is assumed to have various subrelations, like, for example, the relation between a component and its composite (e.g. between a motor and the car the motor is in), the relation between stuff and an object containing this stuff (e.g. between metal and a car), or the relation between a member and a collection it belongs to (e.g. between a tree and the forest this tree belongs to). These pwrelations are subject of several investigations and discussions; see, for example, What is a complete collection of pwrelations? And which of these relations are of importance in a specific application? To help answering some of these questions, we present a scheme to structure pwrelations in 2 The specialisations are not assumed to be disjoint.
Matching in Description Logics with Existential Restrictions
 In Proc. of KR2000
, 2000
"... Matching of concepts against patterns is a new inference task in Description Logics, which was originally motivated by applications of the Classic system. Consequently, the work on this problem was until now mostly concerned with sublanguages of the Classic language, which does not allow for existen ..."
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Cited by 23 (15 self)
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Matching of concepts against patterns is a new inference task in Description Logics, which was originally motivated by applications of the Classic system. Consequently, the work on this problem was until now mostly concerned with sublanguages of the Classic language, which does not allow for existential restrictions. This paper extends the existing work on matching in two directions. On the one hand, the question of what are the most &quot;interesting &quot; solutions of matching problems is explored in more detail. On the other hand, for languages with existential restrictions both, the complexity of deciding the solvability of matching problems and the complexity of actually computing sets of &quot;interesting &quot; matchers are determined. The results show that existential restrictions make these computational tasks more complex. Whereas for sublanguages of Classic both problems could be solved in polynomial time, this is no longer possible for languages with existential restrictions.
Least common subsumer computation w.r.t. cyclic ALNterminologies
 In Proceedings of the 1998 International Workshop on Description Logic, DL'98
, 1998
"... Computing least common subsumers (lcs) and most specific concepts (msc) are inference tasks that can be used to support the "bottom up" construction of knowledge bases for KR systems based on description logic. For the description logic ALN, the msc need not always exist if one res ..."
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Cited by 7 (1 self)
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Computing least common subsumers (lcs) and most specific concepts (msc) are inference tasks that can be used to support the &quot;bottom up&quot; construction of knowledge bases for KR systems based on description logic. For the description logic ALN, the msc need not always exist if one restricts the attention to acyclic concept descriptions. In this paper, we extend the notions lcs and msc to cyclic descriptions, and show how they can be computed. Our approach is based on the automatatheoretic characterizations of fixedpoint semantics for cyclic terminologies developed in previous papers.
Matching Concept Descriptions with Existential Restrictions
, 1999
"... Matching of concepts with variables (concept patterns) is a relatively new operation that has been introduced in the context of description logics, originally to help filter out unimportant aspects of large concepts appearing in industrialstrength knowledge bases. Previous work has concentrated ..."
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Cited by 4 (2 self)
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Matching of concepts with variables (concept patterns) is a relatively new operation that has been introduced in the context of description logics, originally to help filter out unimportant aspects of large concepts appearing in industrialstrength knowledge bases. Previous work has concentrated on (sub)languages of CLASSIC, which in particular do not allow for existential restrictions. In this work, we present sound and complete decision algorithms for the solvability of matching problems and for computing sets of matchers for matching problems in description logics with existential restrictions.
Computing Most Specific Concepts in Description Logics with Existential Restrictions
 LTCSREPORT 0005, LUFG THEORETICAL COMPUTER SCIENCE, RWTH
, 2000
"... Computing the most specific concept (msc) is an inference task that can be used to support the "bottomup" construction of knowledge bases for KR systems based on description logics. For description logics that allow for number restrictions or existential restrictions, the msc need not ..."
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Cited by 3 (0 self)
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Computing the most specific concept (msc) is an inference task that can be used to support the "bottomup" construction of knowledge bases for KR systems based on description logics. For description logics that allow for number restrictions or existential restrictions, the msc need not exist, though. Previous work on this problem has concentrated on description logics that allow for universal value restrictions and number restrictions, but not for existential restrictions. The main new contribution of this paper is the treatment of description logics with existential restrictions. More precisely, we show that, for the description logic ALE (which allows for conjunction, universal value restrictions, existential restrictions, negation of atomic concepts, as well as the top and the bottom concept), and its sublanguages EL (which allows for conjunction, existential restrictions and the topconcept) and EL: (which extends EL by negation of atomic concepts) the msc of an ABoxi...
TBoxes do not yield a compact representation of least common subsumers
, 2001
"... For Description Logics with existential restrictions, the size of the least common subsumer (lcs) of concept descriptions may grow exponentially in the size of the input descriptions. This paper investigates whether the possibly exponentially large concept description representing the lcs can al ..."
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Cited by 2 (1 self)
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For Description Logics with existential restrictions, the size of the least common subsumer (lcs) of concept descriptions may grow exponentially in the size of the input descriptions. This paper investigates whether the possibly exponentially large concept description representing the lcs can always be represented in a more compact way when using an appropriate (acyclic) TBox for defining this description. This conjecture was supported by our experience in a chemical process engineering application.