Abstract
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 mathcal {ALC} with some features amongst I (inverse roles), Q_k (qualified number restrictions with numbers bounded by a constant k), and mathsf {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 types of queries for description logics, introduce interpretation queries, and present some consequences.
Highlights
It is well known that any Boolean function in classical propositional calculus can be learned correctly if the training information system is good enough
We prove that any concept in any description logic that extends the basic Description logics (DLs) ALC with some features amongst I, Qk, and Self can be learned if the training information system is good enough
That class is a bit larger than the one considered in our work, as it allows the features Nk and F, which are special forms of Qk
Summary
It is well known that any Boolean function in classical propositional calculus can be learned correctly if the training information system is good enough. Description logics (DLs) are a family of formal languages suitable for representing and reasoning about terminological knowledge. They are of particular importance in providing a logical formalism for ontologies and the Semantic Web. Binary classification in the context of DLs is called concept learning, as the function to be learned is expected to be characterizable by a concept. Setting 1 Given a knowledge base KB in a description logic L and sets E+ and E− of individuals, learn a concept C in L such that: Vietnam J Comput Sci (2018) 5:3–14. A survey on this subject is beyond the scope of this paper
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