## Description Logics for the Representation of Aggregated Objects (2000)

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Venue: | Proceedings of the 14th European Conference on Artificial Intelligence. IOS |

Citations: | 26 - 4 self |

### BibTeX

@INPROCEEDINGS{Sattler00descriptionlogics,

author = {Ulrike Sattler},

title = {Description Logics for the Representation of Aggregated Objects},

booktitle = {Proceedings of the 14th European Conference on Artificial Intelligence. IOS},

year = {2000},

pages = {239--243},

publisher = {Press}

}

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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 part-whole relations. We discuss properties of part-whole relations and extend the description logic ALC with means for the adequate representation of part-whole relations and thus of aggregated objects. 1 Motivation Description logics are a family of knowledge representation formalisms well-suited for the representation of and reasoning about configurations [27, 21], ontologies [19], and database schemata, where they can support schema design, evolution, and query optimisation [4, 7], source integration in heterogeneous databases/data warehouses [5, 6], and conceptual modeling of multidimensional aggregation [11]. 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...

### Citations

428 | R.: RACER system description
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- 2001
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Citation Context ...mplete. Although this is far more complex than what is commonly assumed to be tractable, it turned out that the corresponding algorithms are amenable to optimisation and behave quite well in practice =-=[3, 14, 13]-=-. The terminological knowledge of an application domain can be fixed in a so-called terminology. Definition 2 A terminological axiom is an expression of the form C v D, where C and D are concepts. A t... |

364 |
Parts: A Study in Ontology
- Simons
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Citation Context ...es, the pw-relation has a variety of properties. For a complete collection of these proper1 LuFG Theoretical Computer Science, RWTH Aachen, Germany, email: sattler@cs.rwth-aachen.de ties, we refer to =-=[25]-=-. Most importantly, the general pw-relation is a strict partial order, i.e., it is transitive and asymmetric (and hence irreflexive). That is, if x part-of y and y part-of z, then x part-of z, and if ... |

332 | S.: Practical reasoning for expressive description logics
- Horrocks, Sattler, et al.
- 1999
(Show Context)
Citation Context ... has-part by part-of \Gamma in the last example yields that Control rod u Faulty is indeed subsumed by 9part-of:Dangerous. Fortunately, it could be shown that reasoning in SI is still PSPACE-complete =-=[16]-=-. Composed Sub-Part-Whole Relations To additionally represent composed pw-relations, we extend SI with role-hierarchies, which allow the user to represent composed part-whole relations as subrolessof ... |

274 | A correspondence theory for terminological logics: Preliminary report
- Schild
- 1991
(Show Context)
Citation Context ... + in concepts of the form 9R + :C and 8R + :C, and define interpretations to interpret R + as the transitive closure of R I . Unfortunately, this extension leads to EXPTIME-completeness of reasoning =-=[22]-=----even with respect to empty terminologies. 2. the transitive orbit of roles [20], whose syntax is defined analogously to the one of the transitive closure. An interpretation is then defined to inter... |

265 | Using an expressive description logic: fact or fiction
- Horrocks
- 1998
(Show Context)
Citation Context ...mplete. Although this is far more complex than what is commonly assumed to be tractable, it turned out that the corresponding algorithms are amenable to optimisation and behave quite well in practice =-=[3, 14, 13]-=-. The terminological knowledge of an application domain can be fixed in a so-called terminology. Definition 2 A terminological axiom is an expression of the form C v D, where C and D are concepts. A t... |

249 | On the decidability of query containment under constraints
- Calvanese, Giacomo, et al.
- 1998
(Show Context)
Citation Context ...isms well-suited for the representation of and reasoning about configurations [27, 21], ontologies [19], and database schemata, where they can support schema design, evolution, and query optimisation =-=[4, 7]-=-, source integration in heterogeneous databases/data warehouses [5, 6], and conceptual modeling of multidimensional aggregation [11]. In all these applications, aggregated objects play a central role,... |

168 | Description logic framework for information integration
- Calvanese, Giacomo, et al.
- 1998
(Show Context)
Citation Context ...rations [27, 21], ontologies [19], and database schemata, where they can support schema design, evolution, and query optimisation [4, 7], source integration in heterogeneous databases/data warehouses =-=[5, 6]-=-, and conceptual modeling of multidimensional aggregation [11]. In all these applications, aggregated objects play a central role, that is, objects that are composed of various parts, which again can ... |

151 |
Attributive Concept Descriptions with Complements
- Schmidt-Schau, Smolka
- 1991
(Show Context)
Citation Context ...fication of pw-relations from [28] into our taxonomy is given in Table 1. 3 Introduction to Description Logics We briefly introduce syntax and semantics of the well-known, basic description logic ALC =-=[24]-=-. Definition 1 Let C be a set of concept names and let R be a set of role names. The set of ALC-concepts is the smallest set such that 1. every concept name is a concept and 2. if C and D are concepts... |

147 | An empirical analysis of optimization techniques for terminological representation systems { or: Making KRIS get a move on
- Baader, Hollunder, et al.
- 1994
(Show Context)
Citation Context ...mplete. Although this is far more complex than what is commonly assumed to be tractable, it turned out that the corresponding algorithms are amenable to optimisation and behave quite well in practice =-=[3, 14, 13]-=-. The terminological knowledge of an application domain can be fixed in a so-called terminology. Definition 2 A terminological axiom is an expression of the form C v D, where C and D are concepts. A t... |

138 | Description logics for conceptual data modeling
- Calvanese, Lenzerini, et al.
- 1998
(Show Context)
Citation Context ...isms well-suited for the representation of and reasoning about configurations [27, 21], ontologies [19], and database schemata, where they can support schema design, evolution, and query optimisation =-=[4, 7]-=-, source integration in heterogeneous databases/data warehouses [5, 6], and conceptual modeling of multidimensional aggregation [11]. In all these applications, aggregated objects play a central role,... |

129 | Augmenting concept languages by transitive closure of roles: An alternative to terminological cycles
- Baader
- 1990
(Show Context)
Citation Context ...under the assumption that has-part is interpreted as a transitive relation. There are basically three possibilities to overcome this shortcoming: We extend ALC with 1. the transitive closure of roles =-=[2]-=-. That is, for a role name R, we allow the use of its transitive closure R + in concepts of the form 9R + :C and 8R + :C, and define interpretations to interpret R + as the transitive closure of R I .... |

127 | A description logic with transitive and inverse roles and role hierarchies
- Horrocks, Sattler
(Show Context)
Citation Context ...tions a part and a whole must satisfy for the component-aggregate relation to hold between them. Second, SHI (as well as SH and SHIQ) has the expressive power for the internalisation of terminologies =-=[2, 15]-=-. This technique polynomially reduces reasoning w.r.t. a (possibly cyclic) terminology to pure concept reasoning. First, we introduce a new transitive role name U 2 R+ and specify that U is a super-ro... |

104 | Part-whole relations in object-centered systems: An overview
- Artale, Franconi, et al.
- 1996
(Show Context)
Citation Context ...tion). Vice versa, to refer to the parts of an object, we use the has-part relation, which is the inverse of the pw-relation, is written has-part, and abbreviated hp-relation. It is commonly believed =-=[1]-=- that only a formalism with very high expressive power can represent pw-relations and aggregated objects adequately. In this paper, we argue in how far the high expressive power of the description log... |

85 | Tbox and Abox reasoning in expressive description logics
- Giacomo, Lenzerini
- 1996
(Show Context)
Citation Context ...d (6nR:C) I = fx j ]fy:hx; yi 2 R I and y 2 C I g 6 ng. 5 Discussion Computational Properties of SHIQ: It is known that reasoning for the highly expressive description logic CIQ 6 is EXPTIME-complete =-=[9]-=-. Now SHIQ is less expressive than CIQ and in the same complexity class, namely EXPTIME-complete (this is a consequence of 4 We assume that R \Gamma \Gamma = R. 5 We use (= 1 R) as a short hand for ( ... |

61 | Combining deduction and model checking into tableaux and algorithms for converse-PDL
- Giacomo, Massacci
(Show Context)
Citation Context ...d thus the ability to internalise terminologies) is PSPACE-complete [16]. Another nice property of the tableau-based algorithm for SHIQ is that it does not have an equivalent to the analytic cut rule =-=[10]-=-, a rule that introduces a large amount of nondeterminism and that is used in satisfiability algorithms in the presence of the transitive closure operator and inverse roles. Expressive power of SHIQ: ... |

53 | Experience Building a Large, Re-usable Medical Ontology using a Description Logic with Transitivity and Concept Inclusions'. cel.tex
- Rector, Horrocks
- 1997
(Show Context)
Citation Context ...f aggregated objects. 1 Motivation Description logics are a family of knowledge representation formalisms well-suited for the representation of and reasoning about configurations [27, 21], ontologies =-=[19]-=-, and database schemata, where they can support schema design, evolution, and query optimisation [4, 7], source integration in heterogeneous databases/data warehouses [5, 6], and conceptual modeling o... |

52 | A concept language extended with different kinds of transitive roles
- Sattler
- 1996
(Show Context)
Citation Context ...rpret R + as the transitive closure of R I . Unfortunately, this extension leads to EXPTIME-completeness of reasoning [22]---even with respect to empty terminologies. 2. the transitive orbit of roles =-=[20]-=-, whose syntax is defined analogously to the one of the transitive closure. An interpretation is then defined to interpret the transitive orbit R \Phi of a role name R as some transitive relation cont... |

41 | A data warehouse conceptual data model for multidimensional aggregation
- Franconi, Sattler
- 2012
(Show Context)
Citation Context ...they can support schema design, evolution, and query optimisation [4, 7], source integration in heterogeneous databases/data warehouses [5, 6], and conceptual modeling of multidimensional aggregation =-=[11]-=-. 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 obj... |

38 |
Subsumption in kl-one is undecidable
- Schmidt-Schauss
- 1989
(Show Context)
Citation Context ...owner v owner) to model this "inheritance " is not a good idea: even for very weak description logics, the extension with role-value maps leads to the undecidability of subsumption and satis=-=fiability [23]-=-. However, there are some restrictions on or variants of role value maps that should be investigated since they might yield decidability of these inference problems. Summing up from what we have said ... |

36 | Finite model reasoning in description logics
- Calvanese
- 1996
(Show Context)
Citation Context ...rithm for finitesmodels would neither be satisfactory. Instead, atomicity requires a reasoning algorithm that decides the existence of a model where part-of is a well-founded, strict partial ordering =-=[8]. Finally,-=- since SHIQ has the tree model property, we cannot model what is called "inheritance along pw-relations". For example, we cannot model that the owner of the reactor is also the owner of the ... |

29 | PSPACE reasoning for graded modal logics
- Tobies
- 2001
(Show Context)
Citation Context ... c-part-of \Gamma In) u (= 1 c-part-of \Gamma Out) Connection u (= 1 c-part-of \Gamma In) u ( 2 c-part-of \Gamma Out) Since number restrictions are mostly "harmless" from an algorithmic poin=-=t of view [26]-=-, we have added them to SHI. Definition 5 A (possibly inverse) role is called simple if it is neither transitive nor has a transitive sub-role. SHIQ is obtained from SHI by allowing, additionally, for... |

13 | Knowledge representation in process engineering
- Baader, Sattler
- 1996
(Show Context)
Citation Context ... relations and thus of aggregated objects. 1 Motivation Description logics are a family of knowledge representation formalisms well-suited for the representation of and reasoning about configurations =-=[27, 21]-=-, ontologies [19], and database schemata, where they can support schema design, evolution, and query optimisation [4, 7], source integration in heterogeneous databases/data warehouses [5, 6], and conc... |

8 |
Modelling physical objects: reasoning about different kinds of parts
- Pribbenow
- 1995
(Show Context)
Citation Context ... between a member and a collection it belongs to (e.g. between a tree and the forest this tree belongs to). These pw-relations are subject of several investigations and discussions; see, for example, =-=[28, 12, 18]-=-. However, various questions concerning pw-relations are still open. Let part-of i denote subrelations of the general pw-relation: ffl How are pw-relations defined, i.e., what is a necessary and suffi... |

5 | Data Integration and Reconciliation in data Warehousing: Conceptual Modeling and Reasoning Support
- Calvanese, Giacomo, et al.
- 1999
(Show Context)
Citation Context ...rations [27, 21], ontologies [19], and database schemata, where they can support schema design, evolution, and query optimisation [4, 7], source integration in heterogeneous databases/data warehouses =-=[5, 6]-=-, and conceptual modeling of multidimensional aggregation [11]. In all these applications, aggregated objects play a central role, that is, objects that are composed of various parts, which again can ... |

5 | A Framework for Part-of Hierarchies - Padgham, Lambrix - 1994 |

4 |
A Taxonomy of Part- Whole Relations
- Winston, Chaffin, et al.
- 1987
(Show Context)
Citation Context ... between a member and a collection it belongs to (e.g. between a tree and the forest this tree belongs to). These pw-relations are subject of several investigations and discussions; see, for example, =-=[28, 12, 18]-=-. However, various questions concerning pw-relations are still open. Let part-of i denote subrelations of the general pw-relation: ffl How are pw-relations defined, i.e., what is a necessary and suffi... |

2 | Using Description Logic for Configuration Problems
- Wache, Kamp
- 1996
(Show Context)
Citation Context ... relations and thus of aggregated objects. 1 Motivation Description logics are a family of knowledge representation formalisms well-suited for the representation of and reasoning about configurations =-=[27, 21]-=-, ontologies [19], and database schemata, where they can support schema design, evolution, and query optimisation [4, 7], source integration in heterogeneous databases/data warehouses [5, 6], and conc... |