Carsten Lutz. Nexp time-complete description logics with concrete domains. ACM Trans. Comput. Logic, 5(4):669--705, 2004.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....introduced by Baader and Hanschke [1] who described a datatype (D) extension of the well known ALC DL. Baader and Hanschke [1] have shown that although the satisfiability of is decidable, if is extended with transitive closure of features, the satisfiability problem is undecidable. Lutz [8] proved that reasoning with and general TBoxes is undecidable. In order to extend expressive DLs with concrete domains, Horrocks and Sattler [7] proposed a simplified approach on concrete domain and applied this approach on the DL. Pan [9] investigated the simplifying constraints of ....

C. Lutz. NExpTime-complete Description Logics with Concrete Domains . LuFG Theoretical Computer Science, RWTH Aachen, Germany, 2000.

....the investigation of suitable DLs in particular, Horrocks and Sattler [8] have presented the DL, along with a sound and complete algorithm for deciding concept satisfiability, a basic reasoning service for DLs and ontologies. A key feature of is that, like DAML OIL, it supports datatypes [1, 8, 9] (e.g. string, integer) as well as the usual abstract concepts (e.g. animal, plant) however, supports a very restricted form of datatypes, i.e. it can only deal with unary datatype predicates. While this is quite close to the requirements of the current version of the DAML OIL language, ....

....introduced by Baader and Hanschke [1] who described a datatype (D) extension of the well known ALC DL. Baader and Hanschke [1] have shown that although the satisfiability of is decidable, if is extended with transitive closure of features, the satisfiability problem is undecidable. Lutz [9] proved that reasoning with and general TBoxes is undecidable. In order to extend expressive DLs http: www.daml.org DAML OIL supports unary datatype predicates and qualified number restrictions with unary datatype predicates. with concrete domains, Horrocks and Sattler [8] proposed a ....

C. Lutz. NExpTime-complete Description Logics with Concrete Domains . LuFG Theoretical Computer Science, RWTH Aachen, Germany, 2000.

.... role age relating (abstract) individuals to their (concrete) age, and a (functional) subrole father of hasParent, the following axiom states that children are younger than their fathers: age father age) 16 Extending expressive DLs with concrete domains may easily lead to undecidability [10, 59]. However, DAML OIL provides only a very limited form of concrete domains. In particular, the concrete domain must not allow for predicates of arity greater than 1 (like in our example) and the predicate restrictions must not contain role chains (like father age in our example) In [67] ....

C. Lutz. NExpTime-complete description logics with concrete domains. In R. Gore, A. Leitsch, and T. Nipkow, editors, Proc. of the Int. Joint Conf. on Automated Reasoning (IJCAR-01), number 2083 in Lecture Notes In Artificial Intelligence, pages 45--60. Springer-Verlag, 2001.

.... calculus RCC 8 [26] have been proposed [7, 16] The addition of a concrete domain to a DL is a rather sensitive operation as far as the preservation of its nice computational properties is concerned: even weak DLs combined with weak concrete domains can become undecidable; see, e.g. [8, 15, 25]. In fact, to investigate DLs with concrete domains is rather hard and requires developing new techniques; cf. 24] ii) Standard DLs have been designed to represent static knowledge which is timeand agent independent. To take into account the dynamic aspects of knowledge, DLs have been extended ....

C. Lutz. NEXPTIME-Complete Description Logics with Concrete Domains. In R. Gore, A. Leitsch and T. Nipkov, editors, Automated Reasoning, Proceedings of the First International Joint Conference (IJCAR'

.... roles is known to be difficult and or highly intractable when combined with either concrete datatypes or named individuals: the concept satisfiability problem is know to be NExpTime hard even for the basic DL ALC augmented with inverse roles and either concrete datatypes or named individuals [Lutz, 2000; Tobies, 2000] This hardness result for concrete datatypes is not yet directly applicable to SHOQ(D) as it depends on comparisons of concrete values (binary predicates) but the addition of such comparisons would be a natural future extension to SHOQ(D) Moreover, the presence of nominals in ....

C. Lutz. Nexptime-complete description logics with concrete domains. In Proceedings of the ESSLLI2000 Student Session, 2000.

.... roles is known to be difficult and or highly intractable when combined with either concrete datatypes or named individuals: the concept satisfiability problem is know to be NExpTime hard even for the basic DL ALC augmented with inverse roles and either concrete datatypes or named individuals [Lutz, 2000; Tobies, 2000] This hardness result for concrete datatypes is not yet directly applicable to SHOQ(D) as it depends on comparisons of concrete values (binary predicates) but the addition of such comparisons would be a natural future extension to SHOQ(D) Moreover, the presence of nominals ....

C. Lutz. Nexptime-complete description logics with concrete domains. In Proceedings of the ESSLLI2000 Student Session, 2000.

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C. Lutz. NExpTime-complete description logics with concrete domains. In R. Gore, A. Leitsch, and T. Nipkow, editors, Proceedings of the First International Joint Conference on Automated Reasoning (IJCAR'01), number 2083.

No context found.

Lutz, C., NExpTime-complete description logics with concrete domains, in: R. Gore, A. Leitsch and T. Nipkow, editors, Proceedings of the First International Joint Conference on Automated Reasoning (IJCAR'01), number 2083.

....if combined with concrete domains: there exist concrete domains Note that the logic already provides for nominals. satisfiability is NExpTime complete. We should like to stress that all NExpTime hardness results obtained in this paper are in accordance with the observation made in [39], namely that the PSpace upper bound for reasoning with is not robust w.r.t. extensions of the logic: there exist several seemingly harmless extensions of (for example acyclic TBoxes and inverse roles) which make the complexity of reasoning leap from PSpace completeness to ....

....# #r. # #R. A # #g. # Step) Step P : g Step ALCK(W) reduction concept C P and key box P . the results obtained for this concrete domain carry over to other, more natural concrete domains based on numbers and arithmetics. The following concrete domain was introduced in [39]. Definition 7 (Concrete domain W) Let # be an alphabet. The concrete domain W is defined by setting #W : # # and defining #W as the smallest set containing the . unary predicates word and nword with word = #W and nword . unary predicates = # and # with = # = # # = # . ....

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C. Lutz. NExpTime-complete description logics with concrete domains. ACM Transactions on Computational Logic, 2002. to appear.

....rather simple (PTIME) concrete domains. We show several variants of this result that depend on other characteristics of key constraints, such as the number of concrete features and the path length . This effect is consistent with the observation that the PSPACE upper bound for is not robust [Lutz, 2003] . Additionally, we prove the NEXPTIME bounds to be tight by presenting tableau algorithms for with key admissible concrete domains that are in NP, where key admissibility is a simple and natural property. We have chosen to devise tableau algorithms since they have the potential to be ....

....) of pairs of words over some alphabet #. A sequence of integers i 1 , i m , with m 1, is called a solution for P iff # i 1 # i m = r i 1 r i m . The problem is to decide whether a given instance P has a solution. # The reduction uses the admissible concrete domain W introduced in [Lutz, 2003] , whose domain is the set of words over # and whose predicates express concatenation of words. For each PCP instance P = # 1 , r 1 ) # k , r k ) we define a concept CP and unary key box such that P has no solution iff CP is satisfiable w.r.t. Intuitively, CP and enforce an ....

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C. Lutz. NExpTime-complete description logics with concrete domains. ACM Transactions on Computational Logic, 2003. To appear.

....h k ) A 1 ) P: In this encoding, paths of length 2 appear inside the concrete domain constructors. Thus, we cannot use ALCQI (D) but have to resort to ALCQI(D) Unfortunately, it is well known that reasoning with ALCQI(D) and general TBoxes is undecidable for a large class of concrete domains [13]. Does this mean that reasoning with RADs and GADs is not possible Certainly not It just means that we have to be very careful in choosing our basic domains and the predicates admitted in RADs and GADs. For the remainder of this section, assume that there exists only a single basic domain: the ....

C. Lutz. NExpTime-complete description logics with concrete domains. In Proc. of IJCAR'01, number

....if reasoning with a concrete domain D is in NP, then reasoning with ALC(D) and all three above extensions (simultaneously) is in NExpTime. We argue that this upper bound captures a large class of interesting concrete domains. This paper is accompanied by a technical report containing full proofs [16]. 2 Description Logics with Concrete Domains We introduce the Description Logics we are concerned with in the remainder of this paper. First, ALCI(D) is de ned which extends ALC(D) with inverse roles. In a second step, we add a role forming concrete domain constructor and obtain the logic ....

....un :P or 9S:E, where S is a complex role. 2. For any 9R:D 2 sub(C) where R is a complex role, sub(D) does not contain any concepts of the form 9u 1 ; un :P or 8S:E, where S is a complex role. Intuitively, these restrictions enforce the nite model property which leads to decidability, see [8, 16] for details. In the remainder of this paper, we assume all ALCRPI(D) concepts to be restricted without further notice. Note that the set of restricted ALCRPI(D) concepts is closed under negation, and, hence, subsumption can be reduced to satis ability. 3 A NExpTime complete Variant of the PCP ....

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C. Lutz. NExpTime-complete description logics with concrete domains. LTCSReport 00-01, LuFG Theoretical Computer Science, RWTH Aachen, Germany, 2000. See http://www-lti.informatik.rwth-aachen.de/Forschung/Reports.html.

....For the temporal perspective, we claim that the combination of general TBoxes and interval based temporal reasoning is important for many application areas. In this paper, we present process engineering as an example. From the concrete domain perspective, our results can be viewed as follows: in [Lutz,2001] , it is shown that, even for very simple concrete domains, reasoning with general TBoxes is undecidable. It was an open question whether there exist interesting concrete domains for which reasoning with general TBoxes is decidable. In this paper, we answer this question to the affirmative. This ....

C. Lutz. NExpTime-complete description logics with concrete domains. In Proc. of IJCAR 2001, LNCS, Siena, Italy, 2001. Springer-Verlag.

....upper bound, we show that, if reasoning with a concrete domain D is in NP, then reasoning with the DL ALCI(D) i.e. the extension of ALC(D) with inverse roles) with acyclic TBoxes is in NExpTime. This paper is accompanied by a technical report which contains all proofs and technical details [9]. 2 2 The Description Logic ALCI(D) In this section, we formally introduce the description logic ALCI(D) with which we are concerned in the remainder of this paper. De nition 1 (Concrete Domain) A concrete domain D = D ; D ) is given by a a set D called the domain and a set of predicate ....

....[8] trying to obtain an expressive logic with concrete domains which is still in PSpace. The second approach is to de ne extensions of ALCI(D) which means that the obtained logics are at least NExpTime hard and that feature (dis)agreements cannot be considered without loosing decidability (in [9], we prove that the DL ALCIF is undecidable) Acknowledgments My thanks go to Franz Baader, Ulrike Sattler, and Stephan Tobies for inspiring discussions. The work in this paper was supported by the DFG Project BA1122 3 1 Combinations of Modal and Description Logics . 10 ....

C. Lutz. NExpTime-complete description logics with concrete domains. LTCS-Report 00-01, LuFG Theoretical Computer Science, RWTH Aachen, Germany, 2000. See http://www-lti.informatik.rwthaachen. de/Forschung/Reports.html.

No context found.

Carsten Lutz. Nexp time-complete description logics with concrete domains. ACM Trans. Comput. Logic, 5(4):669--705, 2004.

No context found.

Carsten Lutz. Nexp time-complete description logics with concrete domains. ACM Trans. Comput. Logic, 5(4):669--705, 2004.

No context found.

C. Lutz. NExpTime-complete Description Logics with Concrete Domains . LuFG Theoretical Computer Science, RWTH Aachen, Germany, 2000.

No context found.

C. Lutz. NExpTime-complete description logics with concrete domains. ACM Transactions on Computational Logic, 2002. to appear.

No context found.

C. Lutz. NExpTime-complete description logics with concrete domains. In Proceedings of the First International Joint Conference on Automated Reasoning (IJCAR '01), number 2083.

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