Carsten Lutz. Reasoning with concrete domains. In Proc. of the 16th Int. Joint Conf. on Artificial Intelligence, pages 90--95. Morgan Kaufmann Publishers Inc., 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... 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 with temporal, dynamic, epistemic and other intentional operators [22, 9, 10, 12, 2, 36, 38] The resulting ....

....8 It is of interest, however, that A satisfiability is not preserved under E connections. More precisely, the following negative result holds, where ALCF is the extension of ALC with functional roles and the same as constructor (it is known that A satisfiability for ALCF is decidable [18, 24] while satisfiability is not [3] Theorem 8. Let S be an arbitrary ADS. Then the A satisfiability problem for any E connection C(ALCF ; S) with a non empty E is undecidable. Before presenting the proofs, we illustrate the notion of E connection with illuminative examples. 4 Examples of ....

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C. Lutz. Reasoning with concrete domains. In T. Dean, editor, Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI'99), pages 90--95, Stockholm, Sweden, 1999. Morgan Kaufmann, Los Altos. 19

....language ALCF(D) The limit of this result is that the encoding preserves only satis ability, and it does not clarify the real relationships between the two languages with respect to the problems of subsumption and logical implication. As far as the computational properties are concerned, Lutz [34] proves that concept satis ability, subsumption and ABox consistency for the logics ALC(D) and ALCF(D) are PSpace complete provided that satis ability in the concrete domain is in PSpace. In the case of ALCRP(D) it has been proved the undecidability of reasoning in the full language [26] ....

C. Lutz, Reasoning with concrete domains, in Proc. of the 16 th IJCAI, pages 90-95, Stockholm, Sweden, 1999.

....: p I n (x) q I 1 (y) q I m (y) 2 P D g The semantics of the additional ABox statements involving concrete predicates follows the obvious intuition. In this framework, assuming a concrete domain composed by temporal intervals and the Allen s predicates proved admissible by [ Lutz, 1999b ] the concept of Mortal can be de ned as follows: Mortal : ALIVE STATE : LivingBeing u DEAD STATE : LivingBeing)u 9(ALIVE STATE HAS TIME; DEAD STATE HAS TIME) meets i.e. a mortal is any individual having the property of being alive at some temporal interval that meets some other ....

Carsten Lutz. Reasoning with concrete domains. In Proc. of the 16 th IJCAI, pages 90-95, Stockholm, Sweden, 1999.

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Lutz, C., Reasoning with concrete domains, in: T. Dean, editor, Proceedings of the Sixteenth International Joint Conference on Arti cial Intelligence (IJCAI'99) (1999), pp. 90-95. 11

....Other DLs with concrete domains can be found in [3, 8, 12] while applications of such logics are described in [2, 8] In this paper, we are interested in the complexity of reasoning with Description Logics providing for concrete domains. The complexity of ALC(D) itself is determined in [14], where reasoning with ALC(D) is proved to be PSpace complete if reasoning with the concrete domain D is in PSpace. However, for many applications, the expressivity of ALC(D) is not sucient which makes it quite natural to consider extensions of this logic with additional means of expressivity. We ....

....we show that the satis ability of ALC(P) concepts w.r.t. TBoxes is NExpTime hard. As already mentioned, this result is rather surprising since (1) satis ability of ALC(D) concepts without reference to TBoxes is known to be PSpace complete if reasoning with the concrete domain D is in PSpace [14], and (2) admitting acyclic TBoxes does usually not increase the complexity of reasoning [13] The proof is by a reduction of the 2 n 1 PCP using the concrete domain P introduced in the previous section. Given a 2 n 1 PCP P = 1 ; r 1 ) k ; r k ) we de ne a TBox TP of size ....

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C. Lutz. Reasoning with concrete domains. In Proc. of IJCAI-99, pp. 90-95, Stockholm, Sweden, July 31 { August 6, 1999. Morgan-Kaufmann Publishers.

....domain concept constructor. More information on concrete domains can, e.g. be found in [ 4; 11; 17 ] In this paper, we are interested in the complexity of reasoning with DLs which provide concrete domains, where reasoning refers to testing satis ability and subsumption of concepts. In [ 20 ] we proved that reasoning with ALC(D) is PSpace complete provided that reasoning with the concrete domain D (i.e. testing the satis ability of nite conjunctions of predicates from D) is in PSpace. However, for many applications, the expressivity of ALC(D) is not sucient and one wants to ....

....TBoxes In this section, we show that the satis ability of ALC(P) concepts w.r.t. TBoxes is NExpTime hard. This result is rather surprising since (1) satis ability of ALC(D) concepts without reference to TBoxes is known to be PSpace complete if reasoning with the concrete domain D is in PSpace [ 20 ] and (2) admitting acyclic TBoxes does usually not increase the complexity of reasoning [ 19 ] The proof is by a reduction of the 2 n 1 PCP using the concrete domain P introduced in the previous section. Given a 2 n 1 PCP P = 1 ; r 1 ) k ; r k ) we de ne a TBox T [P ....

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C. Lutz. Reasoning with concrete domains. In Proceedings of the Sixteenth International Joint Conference on Articial Intelligence IJCAI-99, Stockholm, Sweden, July 31 { August 6, 1999. 54

....domain predicate. The last conjunct of this concept uses the concrete domain constructor to state that the process involves at least one workpiece whose diameter is at least 50 centimeters. In this paper, we are interested in the complexity of reasoning with DLs which provide concrete domains. In [8], we proved that reasoning with ALC(D) is PSpace complete provided that reasoning with the concrete domain D (i.e. testing the satis ability of nite conjunctions of predicates from D) is in PSpace. However, for many applications, the expressivity of ALC(D) is not sucient and one wants to extend ....

....of reasoning with these DLs depends on the complexity of reasoning with the concrete domain D. As the de nition of admissible concrete domains suggests, the task performed by the concrete domain reasoner is usually to decide the satis ability of nite conjunctions of concrete domain predicates [2, 8]. The complexity of this inference will thus be important for establishing complexity results for ALC(D) and ALCI(D) 3.1 2 n 1 PCPs and the Concrete Domain P The lower complexity bounds are established by a reduction of the 2 n 1PCP, a NExpTime complete variant of the well known Post ....

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C. Lutz. Reasoning with concrete domains. In Proceedings of the Sixteenth International Joint Conference on Articial Intelligence IJCAI-99, Stockholm, Sweden, July 31 { August 6, 1999.

....1 Introduction Description Logics (DLs) are formalisms for representing and reasoning about conceptual knowledge. There exist several extensions of DLs for an appropriate integration of temporal knowledge [4] This paper investigates the relation between the two DLs ## #### [2, 3] and ####(#) [10,8]. ## #### is an interval based, temporal DL for reasoning about objects whose properties vary over time. ####(#) is a logic for integrated reasoning about conceptual and so called concrete knowledge. If instantiated with a temporal concrete domain, ####(#)iswell suited for reasoning about ....

....concrete domains provide a means to additionally represent concrete information such as, e.g. numbers or time intervals, and allow for integrated reasoning about both kinds of knowledge. In [6] the basic description logic incorporating concrete domains, ###(#) is introduced. The logic ####(#) [10] extends ###(#) by agreement and disagreement on features. Similar to ###(#) an admissible concrete domain # yields decidabilityof####(#) Before ####(#) is introduced, the de nition of concrete domains is recalled. ######### #### A ######## ###### # is a pair ( # # # ) where # is a set ....

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C. Lutz. Reasoning with concrete domains. In ##### ## ### 16 ## #####, Stockholm, Sweden, July 31 { August 6, 1999.

....1 Introduction Description Logics (DLs) are formalisms for representing and reasoning about conceptual knowledge. There exist several extensions of DLs for an appropriate integration of temporal knowledge [4] This paper investigates the relation between the two DLs T L ALCF [2, 3] and ALCF(D) [10, 8]. T L ALCF is an interval based, temporal DL for reasoning about objects whose properties vary over time. ALCF(D) is a logic for integrated reasoning about conceptual and so called concrete knowledge. If instantiated with a temporal concrete domain, ALCF(D) is well suited for reasoning about ....

....domains provide a means to additionally represent concrete information such as, e.g. numbers or time intervals, and allow for integrated reasoning about both kinds of knowledge. In [6] the basic description logic incorporating concrete domains, ALC(D) is introduced. The logic ALCF(D) [10] extends ALC(D) by agreement and disagreement on features. Similar to ALC(D) an admissible concrete domain D yields decidability of ALCF(D) Before ALCF(D) is introduced, the de nition of concrete domains is recalled. De nition 3.1. A concrete domain D is a pair ( D ; D ) where D is a set ....

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C. Lutz. Reasoning with concrete domains. In Proc. of the 16 th IJCAI, Stockholm, Sweden, July 31 { August 6, 1999.

....the satis ability of ALCF concepts w.r.t. TBoxes can be decided in nondeterministic exponential time. 6 The induced grid may also have the form of a torus since we don t enforce distinct nodes. In this case, however, a tiling of the torus induces a periodic tiling of the rst quadrant. In [ 14 ] , a completion algorithm for deciding satis ability of ALCF(D) concepts w.r.t. empty TBoxes is given which can be executed in polynomial space. ALCF(D) is the extension of ALCF by so called concrete domains. By removing the completion rules and clash conditions dealing with the concrete domain, ....

.... then return inconsistent return consistent de ne procedure feature complete(S) while a rule r from fRu; Rt; Rf9C; Rf8C; R#; R g is applicable to S do S : apply(S; r) return S The correctness of the described algorithm can be easily seen: It corresponds to the algorithm given in [ 14 ] for deciding satis ability of ALCF(D) concepts with all rules and clash triggers concerning the concrete part left out. Since the original algorithm is correct for ALCF(D) it is obviously also correct for ALCF . Furthermore, it can easily be veri ed that, if the original algorithm is started on ....

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C. Lutz. Reasoning with concrete domains. In Proceedings of IJCAI-99, Stockholm, Sweden, July 31 { August 6, 1999. Morgan Kaufmann Publ. Inc., San Mateo, CA, 1999.

....Reasoning Carsten Lutz LTCS Report 99 04 RWTH Aachen LuFg Theoretische Informatik http: www lti.informatik.rwth aachen.de Ahornstr. 55 52074 Aachen Germany On the Complexity of Terminological Reasoning Carsten Lutz RWTH Aachen, LuFG Theoretical Computer Science Ahornstr. 55, 52074 Aachen April 28, 1999 Abstract TBoxes are an important component of knowledge representation systems based on description logics (DLs) since they allow for a natural representation of terminological knowledge. Largely due to a classical result given by Nebel [ 20 ] complexity analyses for DLs have, until now, ....

....ALC(D) and ALCF(D) it is shown that satis ability w.r.t. TBoxes is not in PSpace: For the logic ALCF [ 16 ] i.e. ALC extended by features and feature agreement, it is proved that satis ability w.r.t. TBoxes is a NExpTime complete problem. The logics ALC(D) and ALCF(D) see [ 3 ] and [ 19 ] allow for the integration of logical reasoning with reasoning about concrete data like, e.g. numbers, time intervals or spatial regions. Both logics are parameterized with a concrete domain D. Pure concept satis ability is PSpace complete for both DLs provided that reasoning with the ....

[Article contains additional citation context not shown here]

C. Lutz. Reasoning with concrete domains. In Proceedings of the Sixteenth International Joint Conference on Articial Intelligence IJCAI99, Stockholm, Sweden, July 31 { August 6, 1999.

No context found.

Carsten Lutz. Reasoning with concrete domains. In Proc. of the 16th Int. Joint Conf. on Artificial Intelligence, pages 90--95. Morgan Kaufmann Publishers Inc., 1999.

No context found.

Carsten Lutz. Reasoning with concrete domains. In Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, pages 90--95. Morgan Kaufmann Publishers Inc., 1999.

No context found.

C. Lutz. Reasoning with concrete domains. In Thomas Dean, editor, Proceedings of the Sixteenth International Joint Conference on Arti cial Intelligence IJCAI-99, pages 90-95, Stockholm, Sweden, July 31 { August 6, 1999. Morgan-Kaufmann Publishers.

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