On C-Learnability in Description Logics (original) (raw)
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On the possibility of correct concept learning in description logics
Vietnam Journal of Computer Science
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
Concept Learning in Description Logics
Abstract. In this paper we focus on learning concept descriptions expressed in Description Logics. After stating the learning problem in this context, a FOIL-like algorithm is presented that can be applied to general DL languages, discussing related theoretical aspects of learning with the inherent incompleteness underlying the semantics of this representation. Subsequently we present an experimental evaluation of the implementation of this algorithm performed on some real ontologies in order to empirically assess its performance.
A Model for Learning Description Logic Ontologies Based on Exact Learning
Proceedings of the AAAI Conference on Artificial Intelligence
We investigate the problem of learning description logic (DL) ontologies in Angluin et al.’s framework of exact learning via queries posed to an oracle. We consider membership queries of the form “is a tuple a of individuals a certain answer to a data retrieval query q in a given ABox and the unknown target ontology?” and completeness queries of the form “does a hypothesis ontology entail the unknown target ontology?” Given a DL L and a data retrieval query language Q, we study polynomial learnability of ontologies in L using data retrieval queries in Q and provide an almost complete classification for DLs that are fragments of EL with role inclusions and of DL-Lite and for data retrieval queries that range from atomic queries and EL/ELI-instance queries to conjunctive queries. Some results are proved by non-trivial reductions to learning from subsumption examples.
2013
We study learning of description logic TBoxes in An-gluin et al.’s framework of exact learning via queries. We admit entailment queries (“is a given subsumption entailed by the target TBox?”) and equivalence queries (“is a given TBox equivalent to the target TBox?”), as-suming that the signature and logic of the target TBox are known. We present three main results: (1) TBoxes formulated in DL-Lite with role inclusions and com-posite concepts on the right-hand side of concept inclu-sions can be learned in polynomial time; (2) EL TBoxes with only concept names on the right-hand side of con-cept inclusions can be learned in polynomial time; and (3) EL TBoxes cannot be learned in polynomial time. It follows that non-polynomial time learnability of EL
DL-FOIL concept learning in description logics
2008
In this paper we focus on learning concept descriptions expressed in Description Logics. After stating the learning problem in this context, a FOIL-like algorithm is presented that can be applied to general DL languages, discussing related theoretical aspects of learning with the inherent incompleteness underlying the semantics of this representation. Subsequently we present an experimental evaluation of the implementation of this algorithm performed on some real ontologies in order to empirically assess its performance.
A finite basis theorem for the description logic ALC
2015
The main result of this paper is to prove the existence of a finite basis in the description logic ALC. We show that the set of General Concept Inclusions (GCIs) holding in a finite model has always a finite basis, i.e. these GCIs can be derived from finitely many of the GCIs. This result extends a previous result from Baader and Distel, which showed the existence of a finite basis for GCIs holding in a finite model but for the inexpressive description logics EL and EL_gfp. We also provide an algorithm for computing this finite basis, and prove its correctness. As a byproduct, we extend our finite basis theorem to any finitely generated complete covariety (i.e. any class of models closed under morphism domain, coproduct and quotient, and generated from a finite set of finite models).
Concept Learning for Description Logic-Based Information Systems
2012 Fourth International Conference on Knowledge and Systems Engineering, 2012
The work [1] by Nguyen and Szałas is a pioneering one that uses bisimulation for machine learning in the context of description logics. In this paper we generalize and extend their concept learning method [1] for description logic-based information systems. 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 much more suitable for practical information systems based on description logic than the one of [1]. As further extensions we allow also data roles and the concept constructors "functionality" and "unquantified number restrictions". We formulate and prove an important theorem on basic selectors. We also provide new examples to illustrate our approach.
Theoretical Foundations of Defeasible Description Logics
ArXiv, 2019
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in DLs. Indeed, we also analyse the problem of non-monotonic reasoning in DLs at the level of entailment and present an algorithm for the computation of rational closure of a defeasible ontology. Importantly, our algorithm relies completely on classical entailment and shows t...
Bisimulation-Based Concept Learning in Description Logics
Fundamenta Informaticae
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.