Adding Threshold Concepts to the Description Logic $\mathcal{EL}$

Query Answering for Rough EL Ontologies (Extended Technical Report)

“…In addition, they allow to introduce examples of elements that cannot be distinguished by these approximations. Such approaches have recently been investigated for a more fine-grained setting, where vagueness can be captured by a similarity measure and a proto-typical instance, yielding a vague concept that can be dynamically relaxed or strengthened depending on a similarity threshold (Baader, Brewka, and Fernández Gil 2015)-albeit only for unfoldable TBoxes. In our setting the query language itself allows to relax answers by admitting the indiscernibility relation and the approximation constructors in the query language.…”

“…One of their basic motivations is medical applications (Klein, Mika, and Schlobach 2007; Schlobach, Klein, and Peelen 2007), where, for instance, patients can be indistinguishable by their symptoms or drugs and their generica can be indistinguishable by their active agent. Similarly, they were suggested to enhance the web ontology language OWL (Keet 2010) or to solve the identity matching problem in the linked data cloud (Klein, Mika, and Schlobach 2007;Beek, Schlobach, and van Harmelen 2016). As in database settings, indiscernibility relations for rough DLs can be derived automatically from the data (d'Amato et al 2013;Beek, Schlobach, and van Harmelen 2016) making rough DLs amenable for practical applications.…”

“…Similarly, they were suggested to enhance the web ontology language OWL (Keet 2010) or to solve the identity matching problem in the linked data cloud (Klein, Mika, and Schlobach 2007;Beek, Schlobach, and van Harmelen 2016). As in database settings, indiscernibility relations for rough DLs can be derived automatically from the data (d'Amato et al 2013;Beek, Schlobach, and van Harmelen 2016) making rough DLs amenable for practical applications.…”

“…Another approach for dealing with vagueness is based on fuzzy logic. While fuzzy DLs (Bobillo et al 2015) can express vagueness regarding the concept membership of objects, rough DLs can express granularity of objects. The former DLs can easily turn undecidable (Borgwardt, Distel, and Peñaloza 2015;Borgwardt, Cerami, and Peñaloza 2017), but the latter are always decidable, as long as the underlying classical DL is.…”

On Knowledge Dependence in Weighted Description Logic

“…The obvious next steps, aside from further exploring the formal properties of these operators, consist in studying the behaviour and the possibilities of these operators over real datasets and in studying in more detail nested tooth expressions and their connection to non-linear classification models (and, in particular, to multi-layer perceptrons), and in exploring the connections and similarities between our approach and other approaches to learning over knowledge bases such as [17], [5], [12], [13] and [11]. We also plan to study the relationship between our approach and other extensions of description logics with graded membership values and thresholds such as [2,1]. 7 We hope that a deeper exploration of the correspondence theory between tooth logic, statistical learning and classification models, and concept learning in DL, will not only contribute to these fields individually, but will allow for hybrid frameworks where e.g.…”