## A bottom-up method for the deterministic Horn fragment of the description logic ALC (2006)

Venue: | Proceedings of JELIA 2006, LNAI 4160 |

Citations: | 5 - 5 self |

### BibTeX

@INPROCEEDINGS{Nguyen06abottom-up,

author = {Linh Anh Nguyen},

title = {A bottom-up method for the deterministic Horn fragment of the description logic ALC},

booktitle = {Proceedings of JELIA 2006, LNAI 4160},

year = {2006},

pages = {346--358},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

Abstract. We study the deterministic Horn fragment of ALC, which restricts the general Horn fragment of ALC only in that, the constructor ∀R.C is allowed in bodies of program clauses and queries only in the form ∀∃R.C, which is defined as ∀R.C ⊓∃R.C. We present an algorithm that for a deterministic positive logic program P given as a TBox constructs a finite least pseudo-model I of P such that for every deterministic positive concept C, P | = C iff I validates C (and more strongly, iff I,τ | = C, whereτ is the distinguished object of I and the satisfaction means τ is an instance of C w.r.t. I). Pseudo-interpretations are very similar to (traditional) interpretations, except that they have two interpretation functions for roles, one to deal with the constructor ∃R.C and the other to deal with ∀R.C. They are ordered by comparing the sets of validated positive concepts. Our algorithm runs in time 2 O(n) and returns a pseudo-interpretation of size 2 O(n). Our method is extendable for instance checking w.r.t. knowledge bases containing also an ABox in more expressive description logics. 1

### Citations

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(Show Context)
Citation Context ...l for modeling and reasoning about structured knowledge. In the recent years, the combination of description logics and Horn logic has been studied by a considerable number of researchers (see, e.g., =-=[2,8,6,5,7,3]-=-). In [8], Levy and Rousset developed the CARIN family of representation languages that combines the expressive power of Horn rules and DLs. CARIN knowledge bases contain a DL terminology and a set of... |

216 | An overview of tableau algorithms for description logics. Studia Logica, 2001. To appear. An abridged version appeared in Tableaux 2000, volume 1847
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Citation Context ...he existing techniques of resolution, logic programming, or deductive databases. However, the mostly studied computational method for DLs is the tableau method (see the overview by Baader and Sattler =-=[1]-=-). The work [8] by Levy and Rousset on CARIN also uses the tableau method. The tableau method is essentially different from the bottom-up method (used in deductive databases) because of the “or” split... |

179 | R.: Data complexity of query answering in description logics
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Citation Context ...l for modeling and reasoning about structured knowledge. In the recent years, the combination of description logics and Horn logic has been studied by a considerable number of researchers (see, e.g., =-=[2,8,6,5,7,3]-=-). In [8], Levy and Rousset developed the CARIN family of representation languages that combines the expressive power of Horn rules and DLs. CARIN knowledge bases contain a DL terminology and a set of... |

138 |
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(Show Context)
Citation Context ...hniques of resolution, logic programming, or deductive databases. However, the mostly studied computational method for DLs is the tableau method (see the overview by Baader and Sattler [1]). The work =-=[8]-=- by Levy and Rousset on CARIN also uses the tableau method. The tableau method is essentially different from the bottom-up method (used in deductive databases) because of the “or” splitting rule. The ... |

103 | Data complexity of reasoning in very expressive description logics
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(Show Context)
Citation Context ...l for modeling and reasoning about structured knowledge. In the recent years, the combination of description logics and Horn logic has been studied by a considerable number of researchers (see, e.g., =-=[2,8,6,5,7,3]-=-). In [8], Levy and Rousset developed the CARIN family of representation languages that combines the expressive power of Horn rules and DLs. CARIN knowledge bases contain a DL terminology and a set of... |

22 | Datalog and description logics: Expressive power
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Citation Context |

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Citation Context |

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(Show Context)
Citation Context ...bines the two formalisms by allowing the concepts and roles, defined in the terminology, to appear as predicates in the antecedents of the Horn rules. Some works related with this approach are, e.g., =-=[4,2,5]-=-. Another approach is to study Horn fragments of DLs [6,7,3]. In [6], Grosof et al. introduced the description Horn logic (DHL), which is a restricted fragment of DL, and studied it through a transfor... |

19 | Constructing the least models for positive modal logic programs
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(Show Context)
Citation Context ...|= C. The method is especially useful when P is a knowledge base that rarely changes, while C is a query and varies. The problem of constructing such a model M for P is not trivial at all (see, e.g., =-=[9]-=-). A deterministic positive logic program is a finite set of non-negative concepts of the deterministic Horn fragment. Queries to such a program are deterministic positive concepts, which are positive... |

1 |
The long version of this paper. Available at http://www. mimuw.edu.pl/ ∼ nguyen/nguyen06jelia.pdf
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- 2006
(Show Context)
Citation Context ...hat r(x, x ′ ) holds, I,x|= C implies I ′ ,x ′ |= C. In particular, for every positive concept C, I,τ |= C implies I ′ ,τ ′ |= C. The proofs of this lemma and the following corollary are presented in =-=[10]-=-. Corollary 1. Let P be adeterministic positive logic program and I=〈Δ, τ, C, E, U〉 be a pseudo-model of P. Suppose that for every pseudo-model I ′ =〈Δ ′ ,τ ′ , C ′ , E ′ , U ′ 〉 of P,thereexistsr ⊆ Δ... |