scholarly journals A Proposal for Combining Formal Concept Analysis and Description Logics for Mining Relational Data

2007 ◽  
pp. 51-65 ◽  
Author(s):  
Mohamed Hacene Rouane ◽  
Marianne Huchard ◽  
Amedeo Napoli ◽  
Petko Valtchev
Keyword(s):  
Formal Concept Analysis ◽  
Description Logics ◽  
Concept Analysis ◽  
Relational Data ◽  
Formal Concept

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

2020 ◽  
Vol 34 (3) ◽  
pp. 399-403 ◽  
Author(s):  
Francesco Kriegel
Keyword(s):  
Formal Concept Analysis ◽  
Description Logic ◽  
Description Logics ◽  
Concept Analysis ◽  
Rank Function ◽  
Formal Concept ◽  
Graded Lattice

Abstract My thesis describes how methods from Formal Concept Analysis can be used for constructing and extending description logic ontologies. In particular, it is shown how concept inclusions can be axiomatized from data in the description logics $$\mathcal {E}\mathcal {L}$$ E L , $$\mathcal {M}$$ M , $$\textsf {Horn}$$ Horn -$$\mathcal {M}$$ M , and $$\textsf{Prob}\text{-}\mathcal {E}\mathcal {L}$$ Prob - E L . All proposed methods are not only sound but also complete, i.e., the result not only consists of valid concept inclusions but also entails each valid concept inclusion. Moreover, a lattice-theoretic view on the description logic $$\mathcal {E}\mathcal {L}$$ E L is provided. For instance, it is shown how upper and lower neighbors of $$\mathcal {E}\mathcal {L}$$ E L concept descriptions can be computed and further it is proven that the set of $$\mathcal {E}\mathcal {L}$$ E L concept descriptions forms a graded lattice with a non-elementary rank function.

Relational Data,Formal Concept Analysis, and Graded Attributes

2011 ◽  
pp. 462-489 ◽  
Author(s):  
Radim Belohlavek
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Relational Data ◽  
Future Research ◽  
Formal Concept ◽  
Concept Lattices ◽  
Mathematical Foundations

Formal concept analysis is a particular method of analysis of relational data. Also, formal concept analysis provides elaborate mathematical foundations for relational data. In the course of the last decade, several attempts appeared to extend formal concept analysis to data with graded (fuzzy) attributes. Among these attempts, an approach based on residuated implications plays an important role. This chapter presents an overview of foundations of formal concept analysis of data with graded attributes, with focus on the approach based on residuated implications and on its extensions and particular cases. Presented is an overview of both of the main parts of formal concept analysis, namely, concept lattices and attribute implications, and an overview of the underlying foundations and related methods. In addition to that, the chapter contains an overview of topics for future research.

scholarly journals Continuous Domains in Formal Concept Analysis*

2021 ◽  
Vol 179 (3) ◽  
pp. 295-319
Author(s):  
Longchun Wang ◽  
Lankun Guo ◽  
Qingguo Li
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Continuous Functions ◽  
Formal Context ◽  
Formal Concept ◽  
Contractive Mappings ◽  
Continuous Domains ◽  
Algebraic Domains ◽  
Scott Continuous ◽  
Continuous Domain

Formal Concept Analysis (FCA) has been proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notion of contractive mappings over formal contexts is proposed, which can be viewed as a generalization of interior operators on sets into the framework of FCA. Then, by considering subset-selections consistent with contractive mappings, the notions of attribute continuous formal contexts and continuous concepts are introduced. It is shown that the set of continuous concepts of an attribute continuous formal context forms a continuous domain, and every continuous domain can be restructured in this way. Moreover, the notion of F-morphisms is identified to produce a category equivalent to that of continuous domains with Scott continuous functions. The paper also investigates the representations of various subclasses of continuous domains including algebraic domains and stably continuous semilattices.

The Research of Semantic Web Service Matching Algorithm Based on the Formal Concept Analysis

2013 ◽  
Vol 760-762 ◽  
pp. 1708-1712
Author(s):  
Ying Fang Li ◽  
Ying Jiang Li ◽  
Yan Li ◽  
Yang Bo
Keyword(s):  
Semantic Web ◽  
Web Service ◽  
Formal Concept Analysis ◽  
Service Discovery ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Concept ◽  
Semantic Web Service ◽  
Matching Algorithm ◽  
Service Matching

At present, as the number of web services resources on the network drastically increased, how to quickly and efficiently find the needed services from publishing services has become a problem to resolve. Aiming at the problems of low efficiency in service discovery of traditional web service, the formal concept analysis ( FCA) is introduced into the semantic Web service matching, and a Matching Algorithm based semantic web service is proposed. With considering the concept of limited inheritance,this method introduces the concept of limited inheritance to the semantic similarity calculation based on the concept lattice. It is significant in enhancing the service function matching in practical applications through adjust the calculation.

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