On C-Learnability in Description Logics

et al. 2017

Vietnam J Comput Sci

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It is well known that any Boolean function in classical propositional calculus can be learned correctly if the training information system is good enough. In this paper, we extend that result for description logics. We prove that any concept in any description logic that extends ALC with some features amongst I (inverse roles), Q k (qualified number restrictions with numbers bounded by a constant k), and Self (local reflexivity of a role) can be learned correctly if the training information system (specified as a finite interpretation) is good enough. That is, there exists a learning algorithm such that, for every concept C of those logics, there exists a training information system such that applying the learning algorithm to it results in a concept equivalent to C. For this result, we introduce universal interpretations and bounded bisimulation in description logics and develop an appropriate learning algorithm. We also generalize common

Section: Our Contributionsmentioning

confidence: 99%

Section: Our Contributionsmentioning

confidence: 99%

Section: Our Contributionsmentioning

confidence: 99%

Section: Our Contributionsmentioning

confidence: 99%

Section: Lemma 32 L D Has Only Finitely Many Concepts In the Deg mentioning

confidence: 99%

See 3 more Smart Citations

On the possibility of correct concept learning in description logics

Divroodi¹,

et al. 2017

Vietnam J Comput Sci

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Bisimulation-based concept learning for information systems in description logics

Tran

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

On bisimulations for description logics

Divroodi

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.