## Reducing SHIQ − Description Logic to Disjunctive Datalog Programs (2004)

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### BibTeX

@INPROCEEDINGS{Hustadt04reducingshiq,

author = {Ullrich Hustadt},

title = {Reducing SHIQ − Description Logic to Disjunctive Datalog Programs},

booktitle = {},

year = {2004},

pages = {152--162},

publisher = {AAAI Press}

}

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### Abstract

As applications of description logics proliferate, efficient reasoning with large ABoxes (sets of individuals with descriptions) becomes ever more important. Motivated by the prospects of reusing optimization techniques from deductive databases, in this paper, we present a novel approach to checking consistency of ABoxes, instance checking and query answering, w.r.t. ontologies formulated using a slight restriction of the description logic SHIQ. Our approach proceeds in three steps: (i) the ontology is translated into firstorder clauses, (ii) TBox and RBox clauses are saturated using a resolution-based decision procedure, and (iii) the saturated set of clauses is translated into a disjunctive datalog program. Thus, query answering can be performed using the resulting program, while applying all existing optimization techniques, such as join-order optimizations or magic sets. Equally important, the resolution-based decision procedure we present is for unary coding of numbers worst-case optimal, i.e. it runs in EXPTIME.

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253 | On the power of magic
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Citation Context ...based on the database statistics, estimates the amount of work done for different join orders (Abiteboul, Hull, & Vianu 1995). The second point is addressed by means of the magic sets transformation (=-=Beeri & Ramakrishnan 1987-=-). Roughly speaking, the query is modified so that during its evaluation, a set of relevant facts is derived, and checking original query conditions is limited to this estimation. The magic sets trans... |

213 | Disjunctive Datalog - Eiter, Gottlob, et al. - 1997 |

202 |
Rewrite~Based Equational Theorem Proving with Selection and Simplification. Journal of Logic and Computation. Revised version of
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Citation Context ...isfiable. Since KB and Γ are equi-satisfiable by Lemma 5, the claim of the lemma follows. (⇐) If FF(KB) is unsatisfiable, since hyperresolution with superposition and splitting is sound and complete (=-=Bachmair & Ganzinger 1994-=-), a derivation of an empty clause exists. We now show that each such a derivation can be reduced to a derivation of the empty clause in Γ by sound inference 1 Globally unique means that, for some f a... |

169 | Practical reasoning for very expressive description logics - Horrocks, Sattler, et al. |

162 | Resolution theorem proving
- Bachmair, Ganzinger
- 2001
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Citation Context ...onequational literals A are encoded as A ≈ ⊤ in a multi-sorted setting); and we treat ≈ as having built-in symmetry. Moreover, we assume the reader to be familiar with standard firstorder resolution (=-=Bachmair & Ganzinger 2001-=-). Basic superposition is an optimized version of superposition (a calculus for equational theories (Bachmair &sMapping Concepts to FOL πy(⊤, X)=⊤ πy(⊥, X)=⊥ πy(A, X)=A(X) πy(¬C, X)=¬πy(C, X) πy(C ⊓ D... |

94 | Computing small clause normal forms
- Nonnengart, Weidenbach
- 2001
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Citation Context ...B) is translated into a first-order formula, using the operator π from Table 1, which is then transformed into a set of clauses Ξ(KB). We use structural transformation for the clausal transformation (=-=Nonnengart & Weidenbach 2001-=-; Nivelle, Schmidt, & Hustadt 2000), which is known to be polynomial. 3. BS is applied to ΓT R = Ξ(KB T ∪ KB R), that is, to TBox and RBox clauses of KB. We show that this yields clauses of a rather r... |

73 | Theorem Proving with Ordering and Equality Constrained Clauses
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Citation Context ...uperposition Calculus. The basic superposition calculus has been developed to optimize theorem proving with equality (Bachmair et al. 1995). A similar calculus was developed by Nieuwenhuis and Rubio (=-=Nieuwenhuis & Rubio 1995-=-). We assume a standard notion of first-order clauses with equality: all existential quantifiers have been eliminated using Skolemization; all remaining variables are universally quantified; we only c... |

58 | A superposition decision procedure for the guarded fragment with equality - Ganzinger, Nivelle - 1999 |

42 | Resolution-Based Methods for Modal Logics - Nivelle, Schmidt, et al. |

26 | Binding Propagation Techniques for the Optimization of Bound Disjunctive Queries - Greco |

23 |
On the efciency of subsumption algorithms
- Gottlob, Leitsch
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Citation Context ...g of numbers. Hence, ordering constraints can be checked in polynomial time. In the worst case, a single subsumption check requires exponential time in the number of literals of the clauses involved (=-=Gottlob & Leitsch 1985-=-). Furthermore, a subsumption check is performed at most for each pair of closures. Hence, subsumption checking takes exponential time in |KB|. Each closure can potentially participate in an inference... |

18 | A Principle for Incorporating Axioms into the FirstOrder Translation of Modal Formulae
- Schmidt, Hustadt
(Show Context)
Citation Context ...nsformation may be found in (Tobies 2001), where an algorithm for transforming SHIQ concepts to concepts in a related ALCIQb logic was presented. Another similar transformation has been presented in (=-=Schmidt & Hustadt 2003-=-), where it is demonstrated, among others, how to encode multi-modal logic with transitive modalities K4m into plain multi-modal logic Km. In the following, we use NNF(C) to denote the negation-normal... |

15 | Optimization Strategies for Instance Retrieval
- Haarslev, M¤oller
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Citation Context ...o account the query in the search. These deficiencies have already been acknowledged by the research community, and certain optimization techniques for instance retrieval have already been developed (=-=Haarslev & Möller 2002-=-). However, the performance of query answering is still often not satisfactory. Since techniques for reasoning in deductive databases are nowadays mature, we believe it makes sense to examine how to a... |

1 |
Description Logic to Disjunctive Datalog Programs
- Nieuwenhuis, Rubio
- 1995
(Show Context)
Citation Context ...uperposition Calculus. The basic superposition calculus has been developed to optimize theorem proving with equality (Bachmair et al. 1995). A similar calculus was developed by Nieuwenhuis and Rubio (=-=Nieuwenhuis & Rubio 1995-=-). We assume a standard notion of rst-order clauses with equality: all existential quantiers have been eliminated using Skolemization; all remaining variables are universally quantied; we only cons... |

1 | and Equality Constrained Clauses - Nivelle, Schmidt, et al. |

1 |
Resolution-Based Methods for Modal Logics
- Nonnengart, Weidenbach
- 2001
(Show Context)
Citation Context ...KB) is translated into a rst-order formula, using the operator from Table 1, which is then transformed into a set of clauses (KB). We use structural transformation for the clausal transformation (=-=Nonnengart & Weidenbach 2001-=-; Nivelle, Schmidt, & Hustadt 2000), which is known to be polynomial. 3. BS is applied to T R = (KBT [ KBR), that is, to TBox and RBox clauses of KB . We show that this yields clauses of a rather re... |

1 | Incorporating Axioms into the First-Order Translation of Modal Formulae - Tobies |