A Domain Partitioning Method for Bisimulation-Based Concept Learning in Description Logics

Tran, Thanh-Luong; Nguyen, Linh Anh; Hoang, Thi-Lan-Giao

doi:10.1007/978-3-319-06569-4_22

Cited by 3 publications

(8 citation statements)

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“…It combines and revises the results reported in our conference papers [30,31] to give a full picture on the current state of bisimulation-based concept learning for information systems in DLs. 1 In comparison with [22], we take attributes as basic elements of the language.…”

Section: Introductionmentioning

confidence: 83%

Bisimulation-based concept learning for information systems in description logics

Tran

Nguyen

Hoang

2015

Vietnam J Comput Sci

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In description logic-based information systems, objects are described not only by attributes but also by binary relations between them. This work studies concept learning in such information systems. It extends the bisimulationbased concept learning method of Nguyen and Szałas (Rough sets and intelligent systems. Springer, Berlin, pp 517-543, 2013). We take attributes as basic elements of the language. Each attribute may be discrete or numeric. A Boolean attribute is treated as a concept name. This approach is more general and suitable for practical information systems based on description logic than the one of Nguyen and Szałas (Rough sets and intelligent systems. Springer, Berlin, pp 517-543, 2013). As further extensions, we also allow data roles and the concept constructors "functionality" and "unqualified number restrictions". We formulate and prove an important theorem on basic selectors. We also present a domain partitioning method based on information gain that has been used for our implementation of the method. Apart from basic selectors and simple selectors, we introduce a new kind of selectors, called extended selectors. The evaluation

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Section: Introductionmentioning

confidence: 83%

Bisimulation-based concept learning for information systems in description logics

Tran

Nguyen

Hoang

2015

Vietnam J Comput Sci

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“…Here, we provide two more examples, which use different heuristics for choosing selectors. For more details on such heuristics, we refer the reader to [13,18]. …”

Section: Illustrative Examplesmentioning

confidence: 99%

Bisimulation-Based Concept Learning in Description Logics

Tran

Hoang

et al. 2014

Fundamenta Informaticae

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Concept learning in description logics (DLs) is similar to binary classification in traditional machine learning. The difference is that in DLs objects are described not only by attributes but also by binary relationships between objects. In this paper, we develop the first bisimulation-based method of concept learning in DLs for the following setting: given a knowledge base KB in a DL, a set of objects standing for positive examples and a set of objects standing for negative examples, learn a concept C in that DL such that the positive examples are instances of C w.r.t. KB, while the negative examples are not instances of C w.r.t. KB. We also prove soundness of our method and investigate its C-learnability.

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“…In practice, we prefer as simple as possible definitions for the learned concept. Therefore, it is worth using also other selectors [29,36,37] (despite that they are expressible by the basic selectors over I).…”

Section: Bisimulation-based Concept Learning In Dls Using Settingmentioning

confidence: 99%

“…In [37] Tran et al implemented the bisimulation-based concept learning method of [29,36] (for most of the DLs considered in [29,36]). They presented a domain partitioning method that use information gain and both basic selectors and extended selectors.…”

Section: Bisimulation-based Concept Learning In Dls Using Settingmentioning

confidence: 99%

“…The problems studied in [16] are: preservation of semi-positive concepts with respect to comparisons, the Hennessy-Milner property for comparisons, and minimization of interpretations that preserves semi-positive concepts. -Bisimulation-based concept learning in DLs was studied in [29,36,19,13,35,37]. A survey on these papers is presented in Section 7.3.…”

Section: Introductionmentioning

confidence: 99%

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On bisimulations for description logics

Divroodi

Nguyen

2015

Information Sciences

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Abstract. We study bisimulations for useful description logics. The simplest among the considered logics is ALCreg (a variant of PDL). The others extend that logic with inverse roles, nominals, quantified number restrictions, the universal role, and/or the concept constructor for expressing the local reflexivity of a role. They also allow role axioms. We give results about invariance of concepts, TBoxes and ABoxes, preservation of RBoxes and knowledge bases, and the Hennessy-Milner property w.r.t. bisimulations in the considered description logics. Using the invariance results we compare the expressiveness of the considered description logics w.r.t. concepts, TBoxes and ABoxes. Our results about separating the expressiveness of description logics are naturally extended to the case when instead of ALCreg we have any sublogic of ALCreg that extends ALC. We also provide results on the largest auto-bisimulations and quotient interpretations w.r.t. such equivalence relations. Such results are useful for minimizing interpretations and concept learning in description logics. To deal with minimizing interpretations for the case when the considered logic allows quantified number restrictions and/or the constructor for the local reflexivity of a role, we introduce a new notion called QS-interpretation, which is needed for obtaining expected results. By adapting Hopcroft's automaton minimization algorithm and the Paige-Tarjan algorithm, we give efficient algorithms for computing the partition corresponding to the largest auto-bisimulation of a finite interpretation.

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A Domain Partitioning Method for Bisimulation-Based Concept Learning in Description Logics

Cited by 3 publications

References 9 publications

Bisimulation-based concept learning for information systems in description logics

Bisimulation-based concept learning for information systems in description logics

Bisimulation-Based Concept Learning in Description Logics

On bisimulations for description logics

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