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Computing the Least Common Subsumer in the Description Logic $\mathcal{EL}$ w.r.t. Terminological Cycles with Descriptive Semantics [chapter]

Franz Baader
2003 Lecture Notes in Computer Science  
Computing the least common subsumer (lcs) is one of the most prominent non-standard inference in description logics.  ...  In the present paper, we try to extend this result from concept descriptions to concepts defined in a (possibly cyclic) EL-terminology interpreted with descriptive semantics, which is the usual first-order  ...  Introduction Computing the least common subsumer of concepts can be used in the bottom-up construction of description logic (DL) knowledge bases.  ... 
doi:10.1007/978-3-540-45091-7_8 fatcat:p6ppduc6czd6dctwjfeggb47nu

Least Common Subsumers and Most Specific Concepts in a Description Logic with Existential Restrictions and Terminological Cycles

Franz Baader
2003 International Joint Conference on Artificial Intelligence  
Computing least common subsumers (Ics) and most specific concepts (msc) are inference tasks that can support the bottom-up construction of knowledge bases in description logics.  ...  In description logics with existential restrictions, the most specific concept need not exist if one restricts the attention to concept descriptions or acyclic TBoxes.  ...  Introduction Computing the most specific concept of an individual and the least common subsumer of concepts can be used in the bottom-up construction of description logic (DL) knowledge bases.  ... 
dblp:conf/ijcai/Baader03 fatcat:dzpettnykfcgriw7qd3x7u4xyi

Axiomatization of General Concept Inclusions from Streams of Interpretations with Optional Error Tolerance

Francesco Kriegel
2016 European Conference on Artificial Intelligence  
We propose applications that utilize the infimum and the supremum of closure operators that are induced by structures occuring in the field of Description Logics.  ...  More specifically, we consider the closure operators induced by interpretations as well as closure operators induced by TBoxes, and show how we can learn GCIs from streams of interpretations, and how an  ...  The author gratefully thanks the anonymous reviewers for their constructive hints and helpful remarks.  ... 
dblp:conf/ecai/Kriegel16 fatcat:4byiqzgzwjh2hchqpk7vwqvxky

Matching in description logics

F Baader
1999 Journal of Logic and Computation  
Description logic reasoning can be used both during the design phase, in order to improve the quality of ontologies, and in the deployment phase, in order to exploit the rich structure of ontologies and  ...  In particular, we introduce the description logic SHIQ, which has formed the basis of several well-known ontology languages, including OWL.  ...  In a second step, these concepts are generalized into one concept by computing the least common subsumer of C 1 , . . . , C k , i.e., the least concept description (in the available DL) that subsumes C  ... 
doi:10.1093/logcom/9.3.411 fatcat:oi3ruyvki5ez7c55bzmg2bflna

Hybrid EL-Unification is NP-complete

Franz Baader, Oliver Fernandez Gil, Barbara Morawska
2013 International Workshop on Description Logics  
and descriptive semantics.  ...  Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies.  ...  Its introduction was originally motivated by the fact that the least common subsumer (lcs) w.r.t. a set of GCIs interpreted with descriptive semantics need not exist.  ... 
dblp:conf/dlog/BaaderGM13 fatcat:q4kycmwvrraknpa3sd45yrbx7q

Constructing and Extending Description Logic Ontologies using Methods of Formal Concept Analysis

Francesco Kriegel
2020 Künstliche Intelligenz  
In particular, it is shown how concept inclusions can be axiomatized from data in the description logics EL , M , -M , and -EL .  ...  For instance, it is shown how upper and lower neighbors of EL concept descriptions can be computed and further it is proven that the set of EL concept descriptions forms a graded lattice with a non-elementary  ...  A Lattice-Theoretic View on EL The set of EL concept descriptions ordered by subsumption forms a lattice in which conjunction is the infimum operation and the least common subsumer mapping is the supremum  ... 
doi:10.1007/s13218-020-00673-8 fatcat:4gy3h6pe55c3zgncqf46hbuhj4

Measuring Similarity in Description Logics Using Refinement Operators [chapter]

Antonio A. Sánchez-Ruiz, Santiago Ontañón, Pedro Antonio González-Calero, Enric Plaza
2011 Lecture Notes in Computer Science  
Specifically, similarity of two individuals is assessed by first computing their most specific concepts, then the least common subsumer of these two concepts, and finally measuring their distances in the  ...  This paper presents a novel measure for assessing similarity between individuals represented using Description Logic (DL).  ...  In the EL logic and under the assumption of no cycles we have used Algorithm 2 to compute the MSC of an individual.  ... 
doi:10.1007/978-3-642-23291-6_22 fatcat:2gtiv3djcndolegjsymyyep5wu

Concept-Based Semantic Difference in Expressive Description Logics [chapter]

Rafael S. Gonçalves, Bijan Parsia, Ulrike Sattler
2012 Lecture Notes in Computer Science  
Detecting, much less understanding, the difference between two description logic based ontologies is challenging for ontology engineers due, in part, to the possibility of complex, non-local logic effects  ...  Second, the presence of negation and disjunction make the standard semantic difference too sensitive to change: essentially, any logically effectual change always affects all terms in the ontology.  ...  Similar to the case of the least common subsumer [9] , the presence of disjunction (and negation) trivialises definitions that are meaningful in less expressive logics.  ... 
doi:10.1007/978-3-642-35176-1_7 fatcat:osspift7fzcyxlutfhjkvryspa

Forgetting in General EL Terminologies

Nadeschda Nikitina
2011 International Workshop on Description Logics  
We first show that a uniform interpolant of any EL terminology w.r.t. any signature always exists in EL enriched with least and greatest fixpoint constructors and show how it can be computed by reducing  ...  In this paper, we propose an approach for computing a uniform interpolant for general EL terminologies.  ...  For instance, Baader [2] shows that the structurally similar problems of computing Least Common Subsumer and Most Specific Concept can always be solved in cyclic classical TBoxes w.r.t. to greatest fixpoint  ... 
dblp:conf/dlog/Nikitina11 fatcat:oxx6yp7c7je5bjha6i3eb3qygi

Completion-based generalization inferences for the Description Logic ELOR with subjective probabilities

Andreas Ecke, Rafael Peñaloza, Anni-Yasmin Turhan
2014 International Journal of Approximate Reasoning  
We extend this algorithm to computation algorithms for approximations of (i) the most specific concept, which generalizes a given individual into a concept description, and (ii) the least common subsumer  ...  . / International Journal of Approximate Reasoning of concept descriptions into a single new concept description that subsumes all the input concepts and that is least w.r.t. subsumption.  ...  The role-depth bounded least common subsumer of L s -concept descriptions C 1 , . . . , C n w.r.t.  ... 
doi:10.1016/j.ijar.2014.03.001 fatcat:tlhvh3mc4bhx3o3b2k22cuu2li

Computing Role-Depth Bounded Generalizations in the Description Logic $\mathcal{ELOR}$ [chapter]

Andreas Ecke, Rafael Peñaloza, Anni-Yasmin Turhan
2013 Lecture Notes in Computer Science  
We consider the following two inferences: The least common subsumer (lcs), which computes for a given set of concepts a new concept that subsumes the input concepts and is the least one w.r.t. subsumption  ...  In this paper we describe methods for computing generalizations in the ELfamily with the help of the standard reasoning algorithms.  ...  The least common subsumer of two L s -concepts C 1 , C 2 w.r.t. an L s -TBox T (written: lcs T (C 1 , C 2 )) is the L t -concept description D s.t.: 1.  ... 
doi:10.1007/978-3-642-40942-4_5 fatcat:rgwxrcbsk5fodjceujghgg5gz4

Decidability and Complexity of Fuzzy Description Logics

Franz Baader, Stefan Borgwardt, Rafael Peñaloza
2016 Künstliche Intelligenz  
First approaches for reasoning in FDLs where based either on a reduction to reasoning in classical description logics (DLs) or on adaptations of reasoning approaches for DLs to the fuzzy case.  ...  However, it turned out that these approaches in general do not work if expressive terminological axioms, called general concept inclusions (GCIs), are available in the FDL.  ...  Overall, our decidability and undecidability results cover most of the FDLs with t-norm-based semantics, as long as the underlying DL contains at least EL and some kind of negation constructor.  ... 
doi:10.1007/s13218-016-0459-3 fatcat:kvlgugali5ebdey55yep3zqzcq

Blending under deconstruction

Roberto Confalonieri, Oliver Kutz
2019 Annals of Mathematics and Artificial Intelligence  
As a field, computational creativity concerns itself with theoretical and practical issues in the study of creativity.  ...  We overview and analyse adopted solutions and then focus on open perspectives that address two core problems in computational approaches to conceptual blending: searching for the shared semantic structure  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s10472-019-09654-6 fatcat:43s7pcygd5d3dit7huznp4p7mu

Refinement-Based Similarity Measure over DL Conjunctive Queries [chapter]

Antonio A. Sánchez-Ruiz, Santiago Ontañón, Pedro Antonio González-Calero, Enric Plaza
2013 Lecture Notes in Computer Science  
This paper focuses on measuring similarity in the context of Description Logics (DL), and specifically on similarity between individuals.  ...  than searching in the space of concepts.  ...  Third, given any two queries, their least common subsumer (LCS) is the most specific query which subsumes both.  ... 
doi:10.1007/978-3-642-39056-2_20 fatcat:fmpsd3hbs5hh7evves5jcwmdwe

Chapter 3 Description Logics [chapter]

Franz Baader, Ian Horrocks, Ulrike Sattler
2008 Foundations of Artificial Intelligence  
In this chapter we will introduce description logics, a family of logic-based knowledge representation languages that can be used to represent the terminological knowledge of an application domain in a  ...  After reviewing some of the most prominent applications of description logics, in particular ontology language applications, we will conclude with an overview of other aspects of description logic research  ...  and frames, in that they are equipped with a formal, logic-based semantics.  ... 
doi:10.1016/s1574-6526(07)03003-9 fatcat:wa2lwv7ywrhvpnk3emfqv2pgyu
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