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## Expressive ABox Reasoning with Number Restrictions, Role Hierarchies, and Transitively Closed Roles (1999)

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### Other Repositories/Bibliography

Citations: | 59 - 25 self |

### Citations

353 | Practical reasoning for expressive description logics’, in
- Horrocks, Sattler, et al.
- 1999
(Show Context)
Citation Context ... + [Sattler, 1996] and ALCHfR + [Horrocks, 1998]. The work on these logics has been extended and a tableaux calculus for deciding concept consistency for the language ALCQHIR + has been presented in [=-=Horrocks et al., 1999-=-b]. Another approach is presented in [De Giacomo and Lenzerini, 1996] where the logic CIQ for reasoning with TBoxes and ABoxes is introduced. The reasoning procedures developed for CIQ are based on a ... |

316 |
Elements of the Theory of Computation.
- Papadimitriou, Lewis
- 1981
(Show Context)
Citation Context ... satisfiable, it holds a I # (##n R) I and #{b | (a, b) # R I }# # n. However, it also holds #{b | (a I , b I ) # R I }# > m with m # n. 3 Thus, we can conclude by the Pigeonhole Principle (e.g. see [=-=Lewis and Papadimitriou, 1981-=-, page 26]) that there exist at least two R-successors b i , b j of a such that b I i = b I j . Since I satisfies A, at least one of the two individuals must be a new individual. Let us assume b i # O... |

272 | Using an expressive description logic: FaCT or fiction
- Horrocks
- 1998
(Show Context)
Citation Context ...It is argued that the trade-o# between expressivity and complexity favors the integration of transitively closed roles instead of a transitive closure operator for roles. Other examples are given in [=-=Horrocks, 1998-=-], where the area of medical terminology is discussed. Design studies for the Galen project identified the need for modeling of transitive part-whole, causal and compositional relations, and to organi... |

200 | A.: Decidable reasoning in terminological knowledge representation systems
- Buchheit, Donini, et al.
- 1993
(Show Context)
Citation Context ...orts general concept inclusions. Furthermore, we assume that the unique name assumption holds for ABox individuals. ALCNHR + is an extension of ALCNH that itself can be polynomially reduced to ALCNR [=-=Buchheit et al., 1993-=-] and vice versa. It is possible to rephrase every hierarchy of role names with a set of role conjunctions and vice versa [Buchheit et al., 1993]. Thus, ALCNHR + can also be viewed as an extension of ... |

161 |
Attributive concept descriptions with complements.
- Schmidt-Schauss, Smolka
- 1991
(Show Context)
Citation Context ...he Description Logic ALCNH R + Motivated by the above-mentioned requirements we introduce in this paper an ABox tableaux calculus for the description logic ALCNHR + . It augments the basic logic ALC [=-=Schmidt-Schauss and Smolka, 1991-=-] with number restrictions, role hierarchies, and transitively closed roles. Note that these language features imply the presence of generalized concept inclusions and cyclic concepts. The use of numb... |

133 | A description logic with transitive and inverse roles and role hierarchies
- Horrocks, Sattler
- 1999
(Show Context)
Citation Context ...tion of qualified number restrictions and inverse roles. This is inspired by several recently proposed DLs providing inverse roles (and qualified number restrictions) as a language feature (e.g. see [=-=Horrocks and Sattler, 1999; Hor-=-rocks et al., 1998]). However, as already pointed out in [Horrocks et al., 1998], ALCNHR + extended by inverse roles lacks the finite model property. It is an open problem how the "blocking techn... |

86 | TBox and ABox reasoning in expressive description logics
- Giacomo, Lenzerini
- 1996
(Show Context)
Citation Context .... Recently, the work on these logics has been extended and a tableaux calculus for deciding concept consistency for the language ALCQHIR + has been presented in [11]. Another approach is presented in =-=[2]-=- where the logic CIQ for reasoning with TBoxes and ABoxes is introduced. In comparison to ALCN HR + and the other approaches mentioned above CIQ offers more operators (e.g. the transitive closure) but... |

57 | Optimising description logic subsumption’,
- Horrocks, Patel-Schneider
- 1999
(Show Context)
Citation Context ...rresponding ABox individuals and their assertions (e.g. ABox incoherence). Another di#culty results in the applicability of optimization techniques such as dependency-directed backtracking (e.g. see [=-=Horrocks and Patel-Schneider, 1999-=-] for a discussion of these techniques). The translational approach will need similar information from a concept consistency tester in order to avoid unnecessary backtracking. An ABox tableaux calculu... |

51 | A concept language extended with different kinds of transitive roles’,
- Sattler
- 1996
(Show Context)
Citation Context ...ired to solve practical modeling problems without resorting to ad hoc extensions. The requirements derived from practical applications of DLs ask for even more expressive languages. For instance, in [=-=Sattler, 1996-=-] the need for transitive roles is demonstrated for representing part-whole relations, family relations or partial orders in general. It is argued that the trade-off between expressivity and complexit... |

33 | A description logic with transitive and converse roles and role hierarchies
- Horrocks, Sattler
- 1998
(Show Context)
Citation Context ..., 1996] and ALCHfR + [Horrocks, 1998]. Recently, the work on these logics has been extended and a tableaux calculus for deciding concept consistency for the language ALCHQI R + has been presented in [=-=Horrocks et al., 1999-=-]. However, only tableaux calculi deciding concept consistency have been developed for these logics. Another approach is presented in [De Giacomo and Lenzerini, 1996] where the logic CIQ for reasoning... |

23 | An empirical evaluation of optimization strategies for abox reasoning in expressive description logics
- Haarslev, Möller
- 1999
(Show Context)
Citation Context ...SPR’, ‘WISBER’, ‘CKB’, and ‘FSS’ (using ALCN H with GCIs) are taken from previous DL benchmarks but role hierarchies and domain and/or range restrictions for primitive roles (using GCIs) are restored =-=[4]-=-. The 5 RACE is available from the URL http://kogswww.informatik.uni-hamburg.de/˜moeller/race.html ‘Bike’ KBs (using ALCN H with GCIs) contain configuration knowledge about various types of bicycles. ... |

21 |
Algorithmic Foundations of Terminological Knowledge Representation Systems
- Hollunder
- 1994
(Show Context)
Citation Context ...of expressiveness is also reflected in an increase of the complexity of the tableaux rules. An alternative might be the so-called "precompletion approach " originally developed for the langu=-=age ALCQ [Hollunder, 1994-=-] and recently applied to ALCHR + [Tessaris and Gough, 1999]. The idea behind the precompletion approach is to transform given ABoxes in a way such that ABox satisfiability is reduced to concept satis... |

15 |
A concept language extended with dierent kinds of transitive roles
- Sattler
- 1996
(Show Context)
Citation Context ...ired to solve practical modeling problems without resorting to ad hoc extensions. The requirements derived from practical applications of DLs ask for even more expressive languages. For instance, in [=-=Sattler, 1996-=-] the need for transitive roles is demonstrated for representing part-whole relations, family relations or partial orders in general. It is argued that the trade-o# between expressivity and complexity... |

6 |
User’s guide and reference manual version 1.1
- RACE
- 1999
(Show Context)
Citation Context ...f TBoxes and realization of ABoxes (Bk=Bike, A=ABox) Figure 3: Runtimes for Bike TBoxes and ABoxes. evaluate optimization techniques for this tableaux calculus, the DL system RACE5 has been developed =-=[6]-=-. RACE implements an ALCN HR + reasoner for answering queries concerning ABoxes and TBoxes. It is a successor of HAM-ALC [3]. The RACE architecture incorporates established and novel optimization tech... |

5 | Applying an ALC ABox consistency tester to modal logic SAT problems
- Haarslev, Möller
- 1999
(Show Context)
Citation Context ...chniques for this tableaux calculus, the DL system RACE5 has been developed [6]. RACE implements an ALCN HR + reasoner for answering queries concerning ABoxes and TBoxes. It is a successor of HAM-ALC =-=[3]-=-. The RACE architecture incorporates established and novel optimization techniques for TBox and ABox reasoning [6, 5]. The combined effectiveness of these and other techniques are demonstrated with kn... |

3 |
Optimization techniques for reasoning with expressive ABox and concept expressions
- Haarslev, Möller
- 2000
(Show Context)
Citation Context ...lementation in RACE is a novel approach. Practical reasoning is only possible with the design and implementation ofappropriate optimization techniques. This is supported by recent empirical findings [=-=Haarslev and Möller, 2000-=-] suggesting that RACE dramatically outperforms other known DL reasoners for logics at least as expressive as ALCN HR +. To the best ofour knowledge there currently exists no other ABox DL system with... |

2 |
5 Available from http://kogs-www.informatik.uni-hamburg.de/˜moeller/race.html
- Haarslev, Möller, et al.
- 1999
(Show Context)
Citation Context ...ALCN H R +. Prominent language features of ALCN H R + are number restrictions, role hierarchies, transitively closed roles, and generalized concept inclusions. The ABox description logic system RACE [=-=Haarslev et al., 1999-=-] is based on the calculus for ALCN H R +. An older version of this report appears in: Proceedings of Seventh International Conference on Principles of Knowledge Representation and Reasoning (KR2000),... |