Ontologies have been established for knowledge sharing and are widely used as a means for conceptually structuring domains of interest. With the growing usage of ontologies, the problem of overlapping knowledge in a common domain becomes critical. We propose the new method FCA--MERGE for merging ontologies following a bottom-up approach which offers a structural description of the merging process. The method is guided by application-specific instances of the given source ontologies, that are to be merged. We apply techniques from natural language processing and formal concept analysis to derive a lattice of concepts as a structural result of FCA--MERGE.

We apply mathematical concept analysis in order to modularize legacy code. By analysing the relation between procedures and global variables, a so-called concept lattice is constructed. The paper explains how module structures show up in the lattice, and how the lattice can be used to assess cohesion and coupling between module candidates. Certain algebraic decompositions of the lattice can lead to automatic generation of modularization proposals. The method is applied to several examples written in Modula-2, Fortran, and Cobol; among them a>100kloc aerodynamics program.

A new method is presented for analyzing and reengineering class hierarchies. In our approach, a class hierarchy is processed along with a set of applications that use it, and a fine-grained analysis of the access and subtype relationships between objects, variables and class members is performed. The result of this analysis is again a class hierarchy, which is guaranteed to be behaviorally equivalent to the original hierarchy, but in which each object only contains the members that are required. Our method is semantically well-founded in concept analysis: the new class hierarchy is a minimal and maximally factorized concept lattice that reflects the access and subtype relationships between variables, objects and class members. The method is primarily intended as a tool for finding imperfections in the design of class hierarchies, and can be used as the basis for tools that largely automate the process of reengineering such hierarchies. The method can also be used as a space-optimizing source-to-source transformation that removes redundant fields from objects. A prototype implementation for Java has been constructed, and used to conduct several case studies. Our results demonstrate that the method can provide valuable insights into the usage of the class hierarchy in a specific context, and lead to useful restructuring proposals.

We describe a general technique for identifying modules in legacy code. The method is based on concept analysis --- a branch of lattice theory that can be used to identify similarities among a set of objects based on their attributes. We discuss how concept analysis can identify potential modules using both "positive" and "negative" information. We present an algorithmic framework to construct a lattice of concepts from a program, where each concept represents a potential module. 1 Introduction Many existing software systems were developed using programming languages and paradigms that do not incorporate object-oriented features and design principles. In particular, these systems often lack a modular style, making maintenance and further enhancement an arduous task. The software engineer's job would be less difficult if there were tools that could transform code that does not make explicit use of modules into functionally equivalent object-oriented code that does make use of modules...

Discovering association rules is one of the most important task in data mining. Many efficient algorithms have been proposed in the literature. The most noticeable are Apriori, Mannila's algorithm, Partition, Sampling and DIC, that are all based on the Apriori mining method: pruning the subset lattice (itemset lattice). In this paper we propose an efficient algorithm, called Close, based on a new mining method: pruning the closed set lattice (closed itemset lattice). This lattice, which is a sub-order of the subset lattice, is closely related to Wille's concept lattice in formal concept analysis. Experiments comparing Close to an optimized version of Apriori showed that Close is very efficient for mining dense and/or correlated data such as census style data, and performs reasonably well for market basket style data.

Abstract. Social bookmark tools are rapidly emerging on the Web. In such systems users are setting up lightweight conceptual structures called folksonomies. The reason for their immediate success is the fact that no specific skills are needed for participating. At the moment, however, there exists no foundational research for these systems. We present a formal model and a new search algorithm for folksonomies, called FolkRank, that exploits the structure of the folksonomy. The proposed algorithm is also applied to find communities within the folksonomy and is used to structure search results. All findings are demonstrated on a large scale dataset. 1

In this paper we describe a formal framework for the problem of mining association rules. The theoretical foundation is based on the field of formal concept analysis. A concept is composed of closed subsets of attributes (itemsets) and objects (transactions). We show that all frequent itemsets are uniquely determined by the frequent concepts. We further show how this lattice-theoretic framework can be used to find a small rule generating set, from which one can infer all other association rules. 1

Software reuse is one of the most advertised advantages of object-orientation. Inheritance, in all its forms, plays an important part in achieving greater reuse, at all stages of development. Class hierarchies start taking shape at the analysis level, where classes that share application-significant data and application-meaningful external behavior are grouped under more general classes. At the design level, such hierarchies are augmented with implementation classes, and possibly reorganized to take into account implementation factors such as performance or code reuse [22]. Getting the analysis-level hierarchy "right" is very important for the understandability and traceability of the models and the reusability of the resulting code [22]. In this paper, we propose a formal method that organizes a set of class interfaces into a lattice structure called Galois Lattice [10]. Such a lattice has several advantages including: 1) embodying protocol conformance, 2) supporting an incremental up...

We apply mathematical concept analysis to the problem of infering configuration structures from existing source code. Concept analysis has been developed by German mathematicians over the last years; it can be seen as a discrete analogon to Fourier analysis. Based on this theory, our tool will accept source code, where configuration-specific statements are controlled by the preprocessor. The algorithm will compute a so-called concept lattice, which -- when visually displayed -- allows remarkable insight into the structure and properties of possible configurations. The lattice not only displays fine-grained dependencies between configuration threads, but also visualizes the overall quality of configuration structures according to software engineering principles. The paper presents a short introduction to concept analysis, as well as experimental results on various programs. 1 Introduction A simple and widely used technique for configuration management is the use of the C preprocessor. ...

We introduce the notion of iceberg concept lattices...