Cohen, W., & Hirsh, H. (1994). Learning the CLASSIC description logic: Theoretical and experimental results. Proceedings of Fourth International Conference on Principles of Knowledge Representation and Reasoning (pp. 121--133). Morgan Kaufmann.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and explained their utility to improve the accuracy and efficiency of a system of information agents. An prototype system has been implemented. Future work will include exploring which learning knowledge discovery algorithms provide more useful concept descriptions (for example, results from [1] may be promising) and how to perform the extensional analysis incrementally to better keep track of the evolving information sources. ....

William W. Cohen and Haym Hirsh. Learning the classic description logic: Theoretical and experimental results. In Erik Sandewall Jon Doyle and Pietro Torasso, editors, Priciples of Knowledege Representation And Reasoning. Proceedings of the Fourth International Conference, pages 121-133, Bonn, Germany, 1994.

.... main approaches to represent and reason about relational knowledge, namely description logic (DL) and first order horn logic (HL) In Inductive Logic Programming (ILP) learning first order horn logic is investigated in depth, for learning DLs there exist first approaches [ Kietz and Morik, 1994; Cohen and Hirsh, 1994b ] and theoretical learnability results [ Cohen and Hirsh, 1994a; Frazier and Pitt, 1994 ] Recently, it was proposed to use Carin ALN as a framework for learning [ Rouveirol and Ventos, 2000 ] This is an interesting extension of ILP as provides a new bias orthogonal to the one used in ILP, ....

.... namely description logic (DL) and first order horn logic (HL) In Inductive Logic Programming (ILP) learning first order horn logic is investigated in depth, for learning DLs there exist first approaches [ Kietz and Morik, 1994; Cohen and Hirsh, 1994b ] and theoretical learnability results [ Cohen and Hirsh, 1994a; Frazier and Pitt, 1994 ] Recently, it was proposed to use Carin ALN as a framework for learning [ Rouveirol and Ventos, 2000 ] This is an interesting extension of ILP as provides a new bias orthogonal to the one used in ILP, i.e. it allows all quantified descriptions of body variables, ....

Cohen, W. W. and H. Hirsh: 1994b, `Learning the CLASSIC Description Logic: Theoretical and Experimental Results'. In: Proc. of the Int. Conf. on Knowledge Representation (KR94).

....approaches to represent and reason about relational knowledge, namely description logic and first order horn logic. In Inductive Logic Programming (ILP) learning first order horn logic is investigated in depth, for learning description logics there exist first approaches [Kietz and Morik, 1994; Cohen and Hirsh, 1994b] and theoretical learnability results [Cohen and Hirsh, 1994a; Frazier and Pitt, 1994] Recently, it was proposed to use CARIN 4 J fl as a framework for learning [Rouveirol and Ventos, 2000] This is a very interesting extension of ILP as 4 Jfprovides a new bias orthogonal to the one used in ....

....namely description logic and first order horn logic. In Inductive Logic Programming (ILP) learning first order horn logic is investigated in depth, for learning description logics there exist first approaches [Kietz and Morik, 1994; Cohen and Hirsh, 1994b] and theoretical learnability results [Cohen and Hirsh, 1994a; Frazier and Pitt, 1994] Recently, it was proposed to use CARIN 4 J fl as a framework for learning [Rouveirol and Ventos, 2000] This is a very interesting extension of ILP as 4 Jfprovides a new bias orthogonal to the one used in ILP, i.e. it al lows all quantified descriptions of ....

Cohen, W. W. and H. Hirsh: 1994b, Learning the CLASSIC Description Logic: Theoretical and Experimental Results'. In: Proc. of the Int. Conf. on Knowledge Representation (KR9J).

....and knowledge acquisition in description logics have become very popular issues. There have been di erent approaches like learning as search over the space of possible concepts for completion of T Boxes [Alv98] learning through observation [LL98] and least common subsumer (lcs) for example [CH94, BK98]) Least common subsumers are the most common approach for learning in DL. lcs are appropriate for precise examples and data constructed for bottom up construction of terminologies, because common properties of examples are deductively collected, but is unsuitable for rough and noisy data. The ....

W. Cohen and H. Hirsh. Learning the classic description logic: Theoretical and experimental results. In KR-94, pages 121-133, Bonn, Germany, 1994.

....individuals. We show that GDCs can be constructed from ABox interpolants and present tableau based algorithms. In the recent past learning and knowledge discovery using description logics (DL) have attracted much research. Least common subsumer (lcs) learning has been the most popular approach [3, 1]. lcs learner construct minimal descriptions for the common properties of a set of positively classi ed objects in the ABox which do not instantiate any negative example. Unfortunately it is not always possible to construct such a minimal description, it can easily be seen that the most speci c ....

W. Cohen and H. Hirsh. Learning the classic description logic: Theoretical and experimental results. In KR-94, pages 121-133, Bonn, Germany, 1994.

....number restrictions [13] For all these DLs, except for Classic in case attributes are interpreted as total functions [12] it has turned out that the lcs always exists and that it can e ectively be computed. Prototypical implementations show that the lcs algorithms behave quite well in practice [7, 4]. For the msc, the situation is not that rosy. For DLs allowing for number restrictions or existential restrictions, the msc does not exist in general. Hence, the rst step in the bottom up construction, namely computing the msc, cannot be performed. In [2] it has been shown that for ALN , a ....

W.W. Cohen and H. Hirsh. Learning the classic description logic: Theoretical and experimental results. In Proc. of KR'94, pp 121-132. Morgan Kaufmann, 1994.

.... of two concept descriptions A; B) is the most specific concept description C (expressible in the given description language) that has b as an instance (that subsumes both A and B) For sub languages of the DL used by the system classic [6] both tasks have already been considered in the literature [7, 9, 8]. However, the algorithms described in these papers only compute approximations of the msc of an individual. In fact, for ABoxes with cyclic dependencies between individuals, the msc of a given individual need not exist. Therefore we allow for cyclic concept descriptions (i.e. concepts defined by ....

....in the characterization of the value restriction sets. 5 We conjecture, however, that the instance problem can be decided in PSPACE, and that the msc can be computed in exponential time. To the best of our knowledge, all the existing work on computing the lcs of description logic concepts [7, 9, 8] can only handle acyclic concept descriptions. In addition, the approach for computing the msc proposed by Cohen and Hirsh [9] yields only an approximation of the msc. In fact, since they allow for acyclic descriptions only, they cannot always derive an exact description for the msc. The pragmatic ....

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W. W. Cohen and H. Hirsh. Learning the classic description logic: Theoretical and experimental results. In Proceedings of the Fourth International Conference on Principles of Knowledge Representation and Reasoning (KR'94), pages 121--133, San Francisco, Calif., 1994. Morgan Kaufmann.

....structural subsumption and an automata theoretic approach. Structural subsumption algorithms are efficient methods for deciding subsumption in description logics without full negation, disjunction, and existential restrictions. The structural subsumption algorithm employed by the system classic [5, 6] is based on a specific data structure for representing concept descriptions, called description graphs. In this context, subsumption is reduced to a structural comparison of description graphs. Another approach for deciding subsumption in sub languages of classic can be obtained from the ....

....to a normal form obtained by applying the above equivalence from left to right. Another difference between the two approaches is that they describe decision procedures for subsumption on two different levels of abstraction. The structural subsumption algorithm for Classic is presented in [5, 6] on the level of the data structure (namely, description graphs) used in the implementation. This provides a description of the algorithm that is very close to its actual implementation. Consequently, both the formal description of the algorithm and the proof of its correctness are quite complex ....

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William W. Cohen and Haym Hirsh. Learning the CLASSIC description logic: Theoretical and experimental results. In Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference (KR94). Morgan Kaufmann, 1994.

.... useful information) It can, e.g. be used to introduce the concept of a reactor with cooling jacket by the description Reactor u 9connected to:Cooling Jacket u 8functionality: Vaporize; where Vaporize is a primitive concept (i.e. not further defined) Previous work on how to compute the lcs [ Cohen and Hirsh, 1994; Frazier and Pitt, 1996 ] has concentrated on sub languages of the DL used by the system classic [ Brachman et al. 1991 ] which allows (among other constructors) for value restrictions, but not for existential restrictions. Thus, the main new contribution of the present paper is the treatment ....

....not pose a problem in practice. Our method depends on the characterization of subsumption by homomorphisms on description trees, because this allows us to construct the lcs as the product of the description trees. For sub languages of classic, a similar method has been used to construct the lcs [ Cohen and Hirsh, 1994; Frazier and Pitt, 1996 ] even though the characterization of subsumption (via a structural subsumption algorithm [ Borgida and PatelSchneider, 1994 ] is not explicitly given in terms of homomorphisms. The main difference is that these languages do not allow for existential restrictions. The ....

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W. W. Cohen and H. Hirsh. Learning the classic description logic: Theoretical and experimental results. In Proc. of KR'94. Morgan Kaufmann, 1994.

....Introduction Computing the least common subsumer (lcs) in description logics (DLs) is an inference task first introduced by Cohen, Borgida, and Hirsh [Cohen et al. 1992] for sublanguages of CLASSIC. Since then it has found several applications: as a key operation in inductive learning algorithms [Cohen and Hirsh, 1994] , as a means to measure the similarity of concepts for information retrieval [M oller et al. 1998] and as an operation to support the bottom up construction of DL knowledge bases [Baader and Kusters, 1998; Baader et al. 1999] Roughly speaking, the lcs of a set of concepts is the most ....

....extract the commonalities from given concept descriptions, a task essential for all the mentioned applications. The first lcs algorithms proposed in the literature were applicable to sublanguages of CLASSIC, more precisely, DLs that in particular allow for number restrictions [Cohen et al. 1992; Cohen and Hirsh, 1994] More recently, motivated by the bottom up construction of knowledge bases in a chemical engineering application [Sattler, 1998; von Wedel and Marquardt, 2000] the lcs has been investigated for the DL ALE [Baader et al. 1999] which allows for existential restrictions instead of number ....

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W.W. Cohen and H. Hirsh. Learning the CLASSIC description logic: Theoretical and experimental results. In Proc. of KR'94. Morgan Kaufmann, 1994.

....predicates. A concept is defined as a set of properties satisfied by individuals that are instances of the concept. These properties are expressed by terms that are built 1 Note that comparing the expressive power of DLs and restrictions of First Order Logic used in ILP is still an open issue [CH94b] from atomic concepts and roles and from a set of connectives. Concepts are partially ordered by a subsumption relation which expresses the inclusion relation between concepts and is usually based on a standard model based logical semantics. The basic inference tasks in DLs are determining ....

....connectives. For instance, CLASSIC is the most expressive implemented DL for which the subsumption computation is polynomial according to a non standard semantics. However, this is not enough to guarantee efficient learning in Valiant s sense of PAC learnability [Val84] It has been shown in [CH94b,CH94a] that although CLASSIC is not PAClearnable, some of its subsets are learnable (e.g. C CLASSIC, k core CLASSIC) Because of these results and some complexity results about reasoning in CARIN (see section 6 for a short complexity study) we consider another subset of CLASSIC called ALN . The ....

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W. W. Cohen and H. Hirsh. Learning the CLASSIC description logic: Theoretical and experimental results. In International Conference on Knowledge Representation and Reasoning, pages 121--133. 1994.

....base to the representation and reasoning system [6] Most DL learning stu is related with the computation of the Least Common Subsumer (LCS) introduced in [3] as an adaptation of Relative Least General Generalization to the DL eld. See for example [4, 7] The work of [11] by one hand, and [5] by another, try to acquire a whole theory (using the LCS computation as a subtask) All this DL work, and most ILP one have been done from a concept learning perspective. In this paper I establish a formal framework that addresses the problem of theory learning as a whole, from a quite general ....

William W. Cohen and Haym Hirsh. Learning the classic description logic: Theoretical and experimental results. In John Doyle, E. Sandewall, and P. Torasso, editors, Proceedings of 4th International Conference on Principles of Knowledge Representation and Reasoning, pages 121-133, Bonn, 1994. Morgan Kaufmann.

....Motivation In description logics (DL) the standard inference problems, like the subsumption and the instance problem, are now well investigated. More recently, new types of inference problems have been introduced and investigated, like matching [11, 5, 3] and computing the least common subsumer [13, 14, 2, 7]. In contrast to the standard inferences, algorithms that solve these nonstandard problems produce concept descriptions as output, which are then returned to the user for inspection. For example, in an application in chemical process engineering [9, 22] we try to support the bottom up construction ....

W.W. Cohen and H. Hirsh. Learning the classic description logic: Theoretical and experimental results. In J. Doyle, E. Sandewall, and P. Torasso, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the 4th International Conference (KR'94), pages 121--132. Morgan Kaufmann, 1994.

....languages [Neb90, Baa96, Kus98] On the other hand, structural subsumption algorithms are efficient methods for deciding subsumption of concept descriptions that do not use full negation, disjunction or existential restrictions. The structural subsumption algorithm employed by the system classic [BP94, CH94] is based on a specific data structure for representing concept descriptions, called description graphs. The idea behind is as follows: given two concepts C and D, we translate the concepts into equivalent description graphs GC and GD . A normalization of GC yields the canonical description graph ....

....Let C; D be ALN concepts. D subsumes C (for short C v D) iff C I D I for all interpretations I. C is equivalent to D (for short C j D) iff C v D and D v C, i.e. C I = D I for all interpretations I. 3 3 Syntax and semantics of description graphs Description graphs were introduced in [BP94, CH94] for deciding subsumption of concepts in the terminological knowledge representation system Classic. Classic allows for more constructors than ALN , e.g. equality restrictions on attribute chains by the constructor SAMEAS. Therefore, we confine the notion of description graphs presented in ....

[Article contains additional citation context not shown here]

William W. Cohen and Haym Hirsh. Learning the CLASSIC description logic: Theoretical and experimental results. In Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference (KR94). Morgan Kaufmann, 1994.

....specific concept description C (expressible in the given description language) that has b as an instance (that subsumes C 1 ; Cn ) The second subtask has been thoroughly investigated for several DLs [6, 1, 3, 11, 10] In this paper, we concentrate on the first subtask. It has been shown [7, 1] that for ALN , the msc of an ABox individual need not exist. In [7] the authors circumvent the problem by using certain approximations of the msc. More precisely, instead of the msc of an ABox individual a, they consider the most specific concept C with depth less or equal to a given bound k ....

....that has b as an instance (that subsumes C 1 ; Cn ) The second subtask has been thoroughly investigated for several DLs [6, 1, 3, 11, 10] In this paper, we concentrate on the first subtask. It has been shown [7, 1] that for ALN , the msc of an ABox individual need not exist. In [7], the authors circumvent the problem by using certain approximations of the msc. More precisely, instead of the msc of an ABox individual a, they consider the most specific concept C with depth less or equal to a given bound k such that a is an instance of C. In [1] the authors solve the problem ....

[Article contains additional citation context not shown here]

W.W. Cohen and H. Hirsh. Learning the classic description logic: Theoretical and experimental results. In J. Doyle, E. Sandewall, and P. Torasso, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the 4th International Conference (KR'94), pages 121--132. Morgan Kaufmann, 1994.

No context found.

Cohen, W., & Hirsh, H. (1994). Learning the CLASSIC description logic: Theoretical and experimental results. Proceedings of Fourth International Conference on Principles of Knowledge Representation and Reasoning (pp. 121--133). Morgan Kaufmann.

No context found.

Cohen WW, Hirsh H. Learning the CLASSIC description logic: theoretical and experimental results. Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference (KR'94), p. 121-33.

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William W. Cohen and Haym Hirsh. Learning the CLASSIC description logics: Theoretical and experimental results. In J. Doyle, E. Sandewall, and P. Torasso, editors, Proc. of the 4th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-94), pages 121--133, 1994.

No context found.

William W. Cohen and Haym Hirsh. Learning the CLASSIC description logic: Theoretical and experimental results. In Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference (KR94), pages 121-133, Bonn, Germany, 1994. Morgan Kaufmann.

No context found.

William W. Cohen and Haym Hirsh. Learning the CLASSIC description logics: Theoretical and experimental results. In J. Doyle, E. Sandewall, and P. Torasso, editors, Proc. of the 4th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-94), pages 121--133, 1994.

No context found.

Cohen W.W., H. Hirsh. Learning the CLASSIC description logic: Theoretical and experimental results. KR'94, pp. 121-133.

No context found.

William W. Cohen and Haym Hirsh. Learning the classic description logic: Theoretical and experimental results. In John Doyle, E. Sandewall, and P. Torasso, editors, Proceedings of 4th International Conference on Principles of Knowledge Representation and Reasoning, pages 121-133, Bonn, 1994. Morgan Kaufmann.

No context found.

William W. Cohen and Haym Hirsh. Learning the CLASSIC description logic: Theoretical and experimental results. In Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference (KR94), pages 121-133, Bonn, Germany, 1994. Morgan Kaufmann.

No context found.

W. W. Cohen and H. Hirsh. Learning the CLASSIC description logic: Theoretical and experimental results. In KR-94,1994.

No context found.

W.W. Cohen and H. Hirsh. Learning the classic description logic: Theoretical and experimental results. In J. Doyle, E. Sandewall, and P. Torasso, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the 4th International Conference (KR'94), pages 121-132. Morgan Kaufmann, 1994. 18

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