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.

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 configuration-specific code pieces are controlled by the preprocessor. The algorithm will compute a so-called concept lattice, which —when visually displayed — offers remarkable insight into the structure and properties of possible configurations. The lattice not only displays tine-grained 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.

. 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 worst-case 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...

We present algorithms for horizontal decomposition, subdirect decomposition, and subtensorial decomposition of concept lattices. The implementations of these algorithms are described, and their complexity is investigated. We then apply the decomposition algorithms to reengineering problems in software engineering, and present several examples. It turns out that concept lattice decomposition is useful not only for understanding old software, but also for restructuring it. 1 Introduction Analysing old software has become an important topic in software technology, as there are millions of lines of legacy code which lack proper documentation; due to ongoing modifications, software entropy has increased steadily. If nothing is done, such software will die of old age - and the knowledge embodied in the software is inevitably lost. As a first step in "software geriatry", one must understand the structure of old software and reconstruct abstract concepts from the source code (called "software...

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 full-scale lattice construction algorithm implementing a divide-and-conquer 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 lattice-constructing methods.

this paper. In Section 1, we examine antimatroid closure spaces. In Section 2, we consider a closure operator that has been widely used in digital image processing [25]. This operator, which can be equally well defined on graphs, is not antimatroid; but it is shown in Section 3 that it retains many of the same structural properties, and is closely related to the classic graph-theoretic theme of domination. Finally, in Section 4, we relate these concepts to premise system[30]. 1 Antimatroid Closure Spaces Assume we have a closure operator ' satisfying the usual axioms: 8Y ` U (we let U denote the universe, or entire space) Y ` Y:', X ` Y implies X:' ` Y:', and Y:':' = Y:'. (Notice that we denote all set valued operators with Greek characters, using a postfix dot notation.) A set<F1

In a recent paper, the authors have proved that for lattices A and B with zero, the isomorphism Conc(A ⊗ B) ∼ = Conc A ⊗ Conc B, holds, provided that the tensor product satisfies a very natural condition (of being capped) implying that A ⊗ B is a lattice. In general, A ⊗ B is not a lattice; for instance, we proved that M3 ⊗ F(3) is not a lattice. In this paper, we introduce a new lattice construction, the box product for arbitrary lattices. The tensor product construction for complete lattices introduced by G. N. Raney in 1960 and by R. Wille in 1985 and the tensor product construction of A. Fraser in 1978 for semilattices bear some formal resemblance to the new construction. For lattices A and B, while their tensor product A ⊗ B (as semilattices) is not always a lattice, the box product, A □B, is always a lattice. Furthermore, the box product and some of its ideals behave like an improved tensor product. For example, if A and B are lattices with unit, then the isomorphism Conc(A □B) ∼ = Conc A ⊗ Conc B holds. There are analogous results for lattices A and B with zero and for a bounded lattice A and an arbitrary lattice B. A join-semilattice S with zero is called {0}-representable, if there exists a lattice L with zero such that Conc L ∼ = S. The above isomorphism results yield the following consequence: The tensor product of two {0}-representable semilattices is {0}-representable.

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This paper reports on knowledge extraction using Rhetorical Structure Theory (RST) and Formal Concept Analysis (FCA). The research is multimodal in two ways: (i) it uses a text tagger to identify key terms in free text, these terms are then used as indexation filters over the free text; (ii) it aims to normalise the contents of multiple text sources into a single knowledge base. The aim is semi-automated extraction of semantic content in texts derived from different sources and merging them into a single coherent knowledge base. We use RST ([7]) to automate the identification of discourse markers in multiple texts dealing with a single subject matter. Marcu ([8, 10]) has shown that RST can be used for the semiautomated mark up of natural language texts. Marcu uses discourse trees, useful to store information about the rhetorical structure, and has shown that the identification of discourse markers from prototypical texts can be automated with 88% precision ([9]). We have adapted Marcu's algorithm in our approach. Although our work draws on recent results from natural language processing, progress in that field is not the objective. The research is motivated by the analysis of texts generated by different sources, their translation to a formal knowledge representation followed by a consolidation into a single knowledge corpus. Our interest is in the analysis of this corpus to determine the reliability of information obtained from multiple agencies ([11]) and then to visually navigate this knowledge. This involves FCA ([14, 15, 17, 18, 6]) for browsing and retrieving text documents ([2, 3, 4, 1]). FCA is typically a propositional knowledge representation technique, i.e., it can only express monadic relations. Recently, Wille ([16]) has shown that FCA can be used to repres...

The free distributive completion of a partial complete lattice is the complete lattice that it is freely generated by the partial complete lattice `in the most distributive way'. This can be described as being a universal solution in the sense of universal algebra. Free distributive completions generalize the constructions of tensor products and of free completely distributive complete lattices over partially ordered sets.