Ian Horrocks and Peter F. Patel-Schneider. Optimizing description logic subsumption. Journal of Logic and Computation, 9(3):267--293, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....diagrams in terms of a particular formal logic of the family of Description Logics (DL) DLs have been proposed as successors of semantic network systems like KL ONE, with an explicit model theoretic semantics. The research on these logics has resulted in a number of automated reasoning systems [13, 14, 11], which have been successfully tested in various application domains (see e.g. 17, 18, 16] Our long term goal is to exploit the deductive capabilities of DL systems, and show that effective reasoning can be carried out on UML class diagrams, so as to provide support during the specification ....

....This represents a significant improvement and is a first step towards the development of modeling tools that offer an automated reasoning support to the designer in his modeling activity. We briefly discuss the tasks that can be performed by exploiting the reasoning capabilities of a reasoner [14, 15], and that allow a modeling tool to take over tasks traditionally left to the responsibility of the designer. Such a tool may construct from a class diagram a knowledge base, and manage it in a way completely transparent to the designer. By exploiting the reasoning services various kinds of ....

I. Horrocks and P. F. Patel-Schneider. Optimizing description logic subsumption. J. of Log. and Comp., 9(3):267--293, 1999.

....Great attention is given in this approach to the complexity analysis for the various sublogics, so as to devise suitable optimization techniques and to single out tractable subcases. This approach is the one followed in the design of KRIS [3] and more recently in the design of FaCT [36, 38] DLP [37], and RACE [60] Here we focus on the research that adheres to the fourth approach. This aims at both identifying very expressive Description Logics with decidable associated decision problems, and characterizing the computational complexity of reasoning in such Description Logics. A major ....

I. Horrocks and P. F. Patel-Schneider. Optimizing description logic subsumption. J. of Logic and Computation, 9(3):267--293, 1999.

....in terms of a particular formal logic of the family of Description Logics (DL) DLs 1 have been proposed as successors of semantic network systems like KL ONE, with an explicit model theoretic semantics. The research on these logics has resulted in a number of automated reasoning systems [14, 15, 12], which have been successfully tested in various application domains (see e.g. 18, 19, 17] Our long term goal is to exploit the deductive capabilities of DL systems, and show that effective reasoning can be carried out on UML class diagrams, so as to provide support during the specification ....

....This represents a significant improvement and is a first step towards the development of modeling tools that offer an automated reasoning support to the designer in his modeling activity. We briefly discuss the tasks that can be performed by exploiting the reasoning capabilities of a DLR reasoner [15, 16], and that allow a modeling tool to take over tasks traditionally left to the responsibility of the designer. Such a tool may construct from a class diagram a DLR knowledge base, and manage it in a way completely transparent to the designer. By exploiting the DLR reasoning services various kinds ....

I. Horrocks and P. F. Patel-Schneider. Optimizing description logic subsumption. J. of Log. and Comp., 9(3):267--293, 1999.

....logics tailored towards class based knowledge representation, to carry out various forms of reasoning on UML class diagrams, so as to provide support during the speci cation phase of software development. Recently the research on DLs has resulted in a number of automated reasoning systems [15, 16, 17, 12, 13], that have been successfully tested in various application domains (see e.g. 19, 20, 18] Such systems are candidates to form the core reasoning engine for advanced UML CASE tools. In this paper, we illustrate a formalization of UML class diagrams in terms of DLs [2] In particular, we show ....

I. Horrocks and P. F. Patel-Schneider. Optimizing description logic subsumption. J. of Log. and Comp., 9(3):267-293, 1999.

.... these algorithms lead to acceptable behaviour in practice (Baader et al. 1994) Highly optimised systems such as FaCT (Horrocks, 1998b) DLP (Patel Schneider, 1999) and Race (Haarslev and Moller, 1999) have an even better behaviour, also for benchmark problems in modal logics (Horrocks, 1998a; Horrocks and Patel Schneider, 1999; Haarslev and Moller, 2000a; Horrocks, 2000; Patel Schneider, 2000) Phase 4: Algorithms and efficient systems for very expressive DLs. Motivated by applications (e.g. in the database area) DL researchers started to investigate DLs whose expressive power goes far beyond the one of ALC (e.g. ....

....and first order predicate logics. studia final complete.tex; 14 08 2001; 13:30; p.3 4 Franz Baader and Ulrike Sattler 1994; De Giacomo, 1995; De Giacomo and Lenzerini, 1996) it turned out to be less satisfactory from a practical point of view. In fact, first tests in a database application (Horrocks et al. 1999) showed that the PDL formulae obtained by the translation technique could not be handled by existing efficient implementations of satisfiability algorithms for PDL (Patel Schneider, 1999) To overcome this problem, DL researchers have started to design practical tableau algorithms for very ....

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Horrocks, I. and P. F. Patel-Schneider: 1999, `Optimizing Description Logic Subsumption'. Journal of Logic and Computation 9(3), 267--293.

....of an existing individual. This means, eventually one can reuse an existing individual for expanding an existential quanti cation. The straightforward idea of adding x : to every new individual, however, is very inecient. Therefore the optimizations described by Horrocks and PatelSchneider [6] should be applied here as well. 7 Summary We have shown how a multi modal logic and in particular description logic satis ability checker can be built which takes as an extra input a speci cation of the frame class. The frame class is speci ed as Relational Algebra formulae. The main results ....

Ian Horrocks and Peter Patel-Schneider. Optimizing description logic subsumption. Journal of Logic and Computation, 9(3):267-293, 1999.

....[7] where a calculus working in nondeterministic exponential time is given, and a modi cation of it working in single exponential time is just foreseen. There has been also a substantial work on the implementation of ecient theorem provers for Description Logics including ALC among others, FaCT [43, 42], DLP [61, 42] HAM ALC [36] CRACK [28] KSAT [32, 30] However, in all these implementations but for DLP, usual tableau strategies (which explore one branch at a time) are applied, and in exploring a branch there is no use of inconsistent sets of concepts already discovered in another branch. ....

....working in nondeterministic exponential time is given, and a modi cation of it working in single exponential time is just foreseen. There has been also a substantial work on the implementation of ecient theorem provers for Description Logics including ALC among others, FaCT [43, 42] DLP [61, 42], HAM ALC [36] CRACK [28] KSAT [32, 30] However, in all these implementations but for DLP, usual tableau strategies (which explore one branch at a time) are applied, and in exploring a branch there is no use of inconsistent sets of concepts already discovered in another branch. For DLP, ....

[Article contains additional citation context not shown here]

Horrocks, I., and Patel-Schneider, P. F. Optimizing description logic subsumption. Journal of Logic and Computation 9, 3 (1999), 267-293.

.... tableau algorithms (Kris [5] and Crack [13] demonstrated that (in spite of their high worst case complexity) these algorithms lead to acceptable behaviour in practice [6] Highly optimised systems such as FaCT [30] have an even better behaviour, also for benchmark problems in modal logics [29, 31]. Phase 4: Algorithms and efficient systems for very expressive DLs. Motivated by applications (e.g. in the database area) DL researchers started to investigate DLs whose expressive power goes far beyond the one of ALC (e.g. DLs that do not have the finite model property) First decidability ....

Ian Horrocks and Peter F. Patel-Schneider. Optimizing description logic subsumption. J. of Logic and Computation, 9(3):267--293, 1999.

....al. 1998) In fact, reasoning capabilities become especially important in complex scenarios such as those arising in heterogenous database applications and Data Warehousing. This line of work was among the motivations for developing systems based on expressive description logics (Horrocks, 1998; Horrocks Patel Schneider, 1999), and has lead to further extending the language of description logics to support Information Integration and, more speci cally, the conceptual modeling of Data Warehouses (Calvanese, De Giacomo, Lenzerini, Nardi, Rosati, 1998) 234 Unifying Class Based Representation Formalisms ....

Horrocks, I., & Patel-Schneider, P. F. (1999). Optimizing description logic subsumption. Journal of Logic and Computation, 9 (3), 267-293.

....a normalize then compare approach, which is quite different than standard theorem proving, and relies on finding a normal form for descriptions that detects nested incoherences, explicates implicit concepts, and removes redundancies. A second family of DLs, typified by Crack [BFT95] and iFact [HPSar] is implemented with tableaux like refutation theorem proving techniques, albeit ones specially made for DLs. Recently, several powerful decidable DLs [CGL99] have been identified, which are closely related to Propositional Dynamic Logic; therefore theorem provers of the later could be used for ....

....it. Specifically, there are detailed results about the decidability and computational complexity of reasoning with various subsets of constructors (and restrictions of them) For example, classic [ABM 89] has a complete subsumption algorithm that is O(n 3 ) Also, recent empirical evidence [HPSar] suggests that special optimizations make tableaux techniques work quite fast on normal knowledge bases, though the problem is worst case exponential. 4 A Formal Framework for Integration Integration mappings, which induce interschema assertions, form the core of our framework. The goal is to ....

I. Horrocks and P.F. Patel-Schneider. Optimizing description logic subsumption. J. Logic and Computation, (to appear).

.... of reasoning with various subsets of constructors (and restrictions of them) For example, through judicious choice of concept constructors (versions of the first 11 in the first table on page 3) classic [7] has a complete subsumption algorithm that is O(n 3 ) Also, recent empirical evidence [14] suggests that special optimizations make the other theorem proving techniques work quite fast on normal knowledge bases, though the problem is worst case exponential. Since the full KRSS DL is still known to express only a very limited subset of Predicate Calculus (the 3 variable subset ) for ....

I. Horrocks, P.F. Patel-Schneider, "Optimizing description logic subsumption", J. Logic and Computation, to appear.

....a normalize then compare approach, which is quite di#erent than standard theorem proving, and relies on finding a normal form for descriptions that detects nested incoherences, explicates implicit concepts, and removes redundancies. A second family of DLs, typified by Crack [BFT95] and iFact [HPSar] is implemented with tableaux like refutation theorem proving techniques, albeit ones specially made for DLs. Recently, several powerful decidable DLs [CGL99] have been identified, which are closely related to Propositional Dynamic Logic; therefore theorem provers of the later could be used for ....

....it. Specifically, there are detailed results about the decidability and computational complexity of reasoning with various subsets of constructors (and restrictions of them) For example, classic [ABM 89] has a complete subsumption algorithm that is O(n 3 ) Also, recent empirical evidence [HPSar] suggests that special optimizations make tableaux techniques work quite fast on normal knowledge bases, though the problem is worst case exponential. 4 A Formal Framework for Integration Integration mappings, which induce interschema assertions, form the core of our framework. The goal is to ....

I. Horrocks and P.F. Patel-Schneider. Optimizing description logic subsumption. J. Logic and Computation, (to appear).

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Ian Horrocks and Peter F. Patel-Schneider. Optimizing description logic subsumption. J. of Logic and Computation, 9(3):267--293, 1999.

....the C status of the R neighbours of x by non deterministically adding C or to the labels of R neighbours not already containing one of these concepts. 3 Dependency directed backtracking Dependency directed backtracking, in particular backjumping, is a key optimisation employed by DL systems [12]. The idea of backjumping is to tag concepts in the tableaux expansion tree to indicate any non deterministic choices on which their existence depends. When the algorithm discovers a contradiction or clash (e.g. a node with both C and in its label) the tags can be used to determine the most ....

Ian Horrocks and Peter F. Patel-Schneider. Optimizing description logic subsumption. J. of Logic and Computation, 9(3):267--293, 1999.

....consequence of the KB. the KB satisfiability test is optimal) However, we can use several heuristics to obtain a better behaviour in most of the cases (i.e. practical tractability) We have empirical evidence that axioms in the KB are one of the major cause of practical intractability (see [13]) As seen in Section 3, the query need to be encoded as an axiom only if is rolled up into a variable. When the query is rolled up into an individual name, the query can be transformed into an Abox assertion. Therefore, the choice of node into which a query graph is rolled up can be used to speed ....

Ian Horrocks and Peter F. Patel-Schneider. Optimizing description logic subsumption. J. of Logic and Computation, 9(3):267--293, 1999.

....however, problems can occur that are much too hard to be solved by naive implementations of theoretical algorithms. Modern DL systems, therefore, include a wide range of optimisation techniques, the use of which has been shown to improve typical case performance by several orders of magnitude [29]. These techniques include lazy unfolding, absorption and dependency directed backtracking. Cycle detection techniques known as blocking may be required in order to guarantee termination. 5.1 Lazy Unfolding In an ontology, or DL Tbox, large and complex concepts are seldom described ....

I. Horrocks and P. F. Patel-Schneider. Optimizing description logic subsumption. J. of Logic and Computation, 9(3):267--293, 1999.

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Ian Horrocks and Peter F. Patel-Schneider. Optimizing description logic subsumption. Journal of Logic and Computation, 9(3):267--293, 1999.

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I. Horrocks and P. F. Patel-Schneider. Optimizing description logic subsumption. J. of Log. and Comp., 9(3):267-293, 1999.

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Ian Horrocks and Peter F. Patel-Schneider. Optimizing description logic subsumption. J. of Logic and Computation, 9(3):267-293, 1999.

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Ian Horrocks and Peter F. Patel-Schneider. Optimizing description logic subsumption. J. of Logic and Computation, 9(3):267-293, 1999.

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I. Horrocks and P. F. Patel-Schneider. Optimizing description logic subsumption. J. of Log. and Comp., 9(3):267--293, 1999.

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Ian Horrocks and Peter Patel-Schneider. Optimizing description logic subsumption', Journal of Logic and Computation, Vol 9(3), pp 267-293, 1999.

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