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Reengineering of Configurations Based on Mathematical Concept Analysis
 ACM Transactions on Software Engineering and Methodology
, 1996
"... We apply mathematical concept analysis to the problem of reengineering configurations. Concept analysis will reconstruct a taxonomy of concepts from a relation between objects and attributes. We use concept analysis to infer configuration structures from existing source code. Our tool NORA/RECS will ..."
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Cited by 59 (7 self)
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We apply mathematical concept analysis to the problem of reengineering configurations. Concept analysis will reconstruct a taxonomy of concepts from a relation between objects and attributes. We use concept analysis to infer configuration structures from existing source code. Our tool NORA/RECS will accept source code, where configurationspecific code pieces are controlled by the preprocessor. The algorithm will compute a socalled concept lattice, which —when visually displayed — offers remarkable insight into the structure and properties of possible configurations. The lattice not only displays tinegrained dependencies between configurations, but also visualizes the overall quality of configuration structures according to software engineering principles. In a second step, interferences between configurations can be analyzed in order to restructure or simplify configurations. Interferences showing up in the lattice indicate high coupling and low cohesion between configuration concepts. Source files can then be simplified according to the lattice structure. Finally, we show how governing expressions can be simplified by utilizing an isomorphism theorem of mathematical concept analysis.
A fast algorithm for building lattices
 Information Processing Letters
, 1999
"... This paper presents a simple, efficient algorithm to compute the covering graph of the lattice generated by a family B of subsets of a set X. The implementation of this algorithm has O..jXj C jBj / jBj / time complexity per lattice element. This improves previous algorithms of Bordat (1986), Gante ..."
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This paper presents a simple, efficient algorithm to compute the covering graph of the lattice generated by a family B of subsets of a set X. The implementation of this algorithm has O..jXj C jBj / jBj / time complexity per lattice element. This improves previous algorithms of Bordat (1986), Ganter and Kuznetsov (1998) and Jard et al. (1994). This algorithm can be used to compute the Galois (concept) lattice, the maximal antichains lattice or the Dedekind–MacNeille completion of a partial
Formal concept analysis as mathematical theory of concepts and concept hierarchies
 Formal Concept Analysis, Foundations and Applications
, 2005
"... Abstract. Formal Concept Analysis has been originally developed as a subfield of Applied Mathematics based on the mathematization of concept and concept hierarchy. Only after more than a decade of development, the connections to the philosophical logic of human thought became clearer and even later ..."
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Abstract. Formal Concept Analysis has been originally developed as a subfield of Applied Mathematics based on the mathematization of concept and concept hierarchy. Only after more than a decade of development, the connections to the philosophical logic of human thought became clearer and even later the connections to Piaget’s cognitive structuralism which Thomas Bernhard Seiler convincingly elaborated to a comprehensive theory of concepts in his recent book [Se01]. It is the main concern of this paper to show the surprisingly rich correspondences between Seiler’s multifarious aspects of concepts in the human mind and the structural properties and relationships of formal concepts in Formal Concept Analysis. These correspondences make understandable, what has been experienced in a great multitude of applications, that Formal Concept Analysis may function in the sense of transdisciplinary mathematics, i.e., it allows mathematical thought to aggregate with other ways of thinking and thereby to support human thought and action. 1 Formal Concept Analysis, Mathematics, and Logic Formal Concept Analysis had its origin in activities of restructuring mathematics, in particular mathematical order and lattice theory. In the initial paper [Wi82], restructuring lattice theory is explained as “an attempt to reinvigorate connections with our general culture by interpreting the theory as concretely as possible, and in this way to promote better communication between lattice theorists and potential users of lattice theory. ” Since then, Formal Concept Analysis has been developed as a subfield of Applied Mathematics based on the mathematization of concepts and concept hierarchies. Only after more than a decade of development, the connections to Philosophical Logics of human thought became clearer, mainly through Charles Sanders Peirce’s late philosophy. Even our general understanding of mathematics did improve as pointed out in the recent paper “Kommunikative Rationalität, Logik und Mathematik ” (“Communicative Rationality, Logic, and Mathematics”) [Wi02b]. The concern of that paper is to explain and to substantiate the following thesis:
Computing a Minimal Representation of the Subsumption Lattice of All Conjunctions of Concepts Defined in a Terminology
 Proc. Intl. KRUSE Symposium
, 1995
"... . For a given TBox of a terminological KR system, the classification algorithm computes (a representation of) the subsumption hierarchy of all concepts introduced in the TBox. In general, this hierarchy does not contain sufficient information to derive all subsumption relationships between conjuncti ..."
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. For a given TBox of a terminological KR system, the classification algorithm computes (a representation of) the subsumption hierarchy of all concepts introduced in the TBox. In general, this hierarchy does not contain sufficient information to derive all subsumption relationships between conjunctions of these concepts. We show how a method developed in the area of "formal concept analysis " for computing minimal implication bases can be used to determine a minimal representation of the subsumption hierarchy between conjunctions of concepts introduced in a TBox. To this purpose, the subsumption algorithm must be extended such that it yields (sufficient information about) a counterexample in cases where there is no subsumption relationship. For the concept language ALC, this additional requirement does not change the worstcase complexity of the subsumption algorithm. One advantage of the extended hierarchy is that it is a lattice, and not just a partial ordering. 1 Introduction In kn...
Managing Complex Objects
, 1994
"... Data Type 87 3.1 Member: A Hierarchy Primitive : : : : : : : : : : : : : : : : : : : : : 88 3.2 Insert: A Primitive for Constructing Hierarchies : : : : : : : : : : : : 89 3.3 Delete: Retracting Objects from Hierarchies : : : : : : : : : : : : : : 90 3.4 Subset: Hierarchy Match : : : : : : : : : : ..."
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Cited by 23 (8 self)
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Data Type 87 3.1 Member: A Hierarchy Primitive : : : : : : : : : : : : : : : : : : : : : 88 3.2 Insert: A Primitive for Constructing Hierarchies : : : : : : : : : : : : 89 3.3 Delete: Retracting Objects from Hierarchies : : : : : : : : : : : : : : 90 3.4 Subset: Hierarchy Match : : : : : : : : : : : : : : : : : : : : : : : : : 92 3.5 Union: Hierarchy Merge : : : : : : : : : : : : : : : : : : : : : : : : : 94 3.6 Intersection: Hierarchy Unification : : : : : : : : : : : : : : : : : : : 97 3.7 Summary : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 99 4 Analysis of Hierarchies for Efficient Search 101 4.1 Ancestor Search using Intersection of Descendants : : : : : : : : : : : 102 4.2 Descendant Search using Unification : : : : : : : : : : : : : : : : : : 113 4.3 Factored Search : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 114 4.3.1 Experiments : : : : : : : : : : : : : : : : : : : : : : : : : : : : 122 4.4 Summary : : : : : : : : : : : : : : : : : : : :...
The ToscanaJ suite for implementing Conceptual Information Systems
 Formal Concept Analysis – State of the Art, Berlin – Heidelberg
, 2004
"... Abstract. For over a decade, work on Formal Concept Analysis has been accompanied by the development of the Toscana software. Toscana was implemented to realize the idea of Conceptual Information Systems which allow the analysis of data using conceptoriented methods. Over the years, many ideas from ..."
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Abstract. For over a decade, work on Formal Concept Analysis has been accompanied by the development of the Toscana software. Toscana was implemented to realize the idea of Conceptual Information Systems which allow the analysis of data using conceptoriented methods. Over the years, many ideas from Formal Concept Analysis have been tested in Toscana systems while the realworld problems encountered led to new theoretical research. After ten years of development, the ToscanaJ project was initiated to solve some outstanding problems of the older Toscana versions. The ToscanaJ suite provides programs for creating and using Conceptual Information Systems. The experience with older Toscana implementations has been applied to the design of the programs. A workflow that developed through many Toscana projects has now been integrated into the tools to make them easier to use. Implemented as an OpenSource project and embedded into the larger Tockit project, ToscanaJ is also a starting point for creating a common base for software development for Formal Concept Analysis. In this paper, we present the features of the ToscanaJ suite and how they can be used to implement Conceptual Information Systems. 1
Combining formal concept analysis and ripple down rules to support reuse. in Software Engineering Knowledge Engineering SEKE'97
"... Abstract: Ripple down rules have addressed two of the major limitations of first generation Expert Systems (ES), the maintenance and knowledge acquisition (KA) bottleneck problems. This is achieved through acquiring knowledge directly from an expert, the use of an exception structure for knowledge r ..."
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Abstract: Ripple down rules have addressed two of the major limitations of first generation Expert Systems (ES), the maintenance and knowledge acquisition (KA) bottleneck problems. This is achieved through acquiring knowledge directly from an expert, the use of an exception structure for knowledge representation and the storing of the cornerstone case associated with each rule. Just as RDR has offered a paradigm shift in the way these problems were solved, it is expected that RDR can offer a new approach to the issue of knowledge reuse. Due the poor acceptance of ES by endusers, our focus is more on reusing knowledge in different modes, such as explanation, critiquing or ‘whatif ’ within the same domain rather than the more conventional approach of reusing problemsolving methods or ontologies to solve a similar problem in a somewhat differerent domain. An evaluation of RDR for reuse showed that many modes of use were possible without any change to the knowledge or its structure but that some modes required understanding of the models represented. Since RDR does not require analysis or modeling of the domain for KA, maintenance or finding conclusions we have incorporated ideas from Formal Concept Analysis (FCA) to allow concepts and the relationships between them to be identified and explored. The addition of FCA tools to RDR is described in this paper. 1. The Reuse of Knowledge The reuse of knowledge should result in potential savings
Conceptual OnLine Analytical Processing
 Information Organization and Databases, chapter 14
, 2002
"... A Conceptual Information System consists of a database together with conceptual hierarchies. The visualization of arbitrary combinations of conceptual hierarchies by nested line diagrams allows an online interaction with a database to analyze data conceptually. The chapter describes the conception ..."
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Cited by 15 (7 self)
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A Conceptual Information System consists of a database together with conceptual hierarchies. The visualization of arbitrary combinations of conceptual hierarchies by nested line diagrams allows an online interaction with a database to analyze data conceptually. The chapter describes the conception of Conceptual Information Systems and discusses the use of their visualization techniques for OnLine Analytical Processing (OLAP).
A PartitionBased Approach towards Constructing Galois (Concept) Lattices
 Discrete Mathematics
, 2002
"... Galois lattices and formal concept analysis of binary relations have proved useful in the resolution of many problems of theoretical or practical interest. Recent studies of practical applications in data mining and software engineering have put the emphasis on the need for both efficient and fle ..."
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Galois lattices and formal concept analysis of binary relations have proved useful in the resolution of many problems of theoretical or practical interest. Recent studies of practical applications in data mining and software engineering have put the emphasis on the need for both efficient and flexible algorithms to construct the lattice. Our paper presents a novel approach for lattice construction based on the apposition of binary relation fragments. We extend the existing theory to a complete characterization of the global Galois (concept) lattice as a substructure of the direct product of the lattices related to fragments. The structural properties underlie a procedure for extracting the global lattice from the direct product, which is the basis for a fullscale lattice construction algorithm implementing a divideandconquer strategy. The paper provides a complexity analysis of the algorithm together with some results about its practical performance and describes a class of binary relations for which the algorithm outperforms the most efficient latticeconstructing methods.