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Using Concept Lattices to Uncover Causal Dependencies in Software
 Proc. Int. Conf. on Formal Concept Analysis, Springer LNAI #3874
, 2006
"... Abstract. Suppose that whenever event x occurs, a second event y must subsequently occur. We say that x “causes ” y, or y is causally dependent on x. Deterministic causality abounds in software where execution of one routine can necessarily force execution of a subsequent subroutine. Discovery of su ..."
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Abstract. Suppose that whenever event x occurs, a second event y must subsequently occur. We say that x “causes ” y, or y is causally dependent on x. Deterministic causality abounds in software where execution of one routine can necessarily force execution of a subsequent subroutine. Discovery of such causal dependencies can be an important step to understanding the structure of undocumented, legacy code. In this paper we describe a methodology based on formal concept analysis that uncovers possible causal dependencies in execution trace streams. We first walk through the process using a small synthetic, but easily comprehensible, example. Then we illustrate its potential using 57 threads involving 18,969 executed operations that were monitored in an open source middleware system. 1
A Generic Scheme for the Design of Efficient OnLine Algorithms for Lattices
"... A major issue with large dynamic datasets is the processing of small changes in the input through correspondingly small rearrangements of the output. This was the motivation behind the design of incremental or online algorithms for lattice maintenance, whose work amounts to a gradual construction o ..."
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Cited by 5 (5 self)
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A major issue with large dynamic datasets is the processing of small changes in the input through correspondingly small rearrangements of the output. This was the motivation behind the design of incremental or online algorithms for lattice maintenance, whose work amounts to a gradual construction of the final lattice by repeatedly adding rows/columns to the data table. As an attempt to put the incremental trend on strong theoretical grounds, we present a generic algorithmic scheme that is based on a detailed analysis of the lattice transformation triggered by a row/column addition and of the underlying substructure. For each task from the scheme we suggest an efficient implementation strategy and put a lower bound on its worstcase complexity. Moreover, an...
Formal Concept Analysis applications to Requirements Engineering and Design
, 2004
"... I declare that the work presented in this thesis is, to the best of my knowledge and belief, original and my own work, except as acknowledged in the text, and that the material has not been submitted, either in whole or in part, for a degree at this or any other university. Thomas Tilley, B.Sc.(Math ..."
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I declare that the work presented in this thesis is, to the best of my knowledge and belief, original and my own work, except as acknowledged in the text, and that the material has not been submitted, either in whole or in part, for a degree at this or any other university. Thomas Tilley, B.Sc.(Maths & Comp. Sc.), B.Info.Tech.(Hons)
ESTABLISHING LOGICAL RULES FROM EMPIRICAL DATA
, 2008
"... We review a method of generating logical rules, or axioms, from empirical data. This method, using closed set properties of formal concept analysis, has been previously described and tested on rather large sets of deterministic data. In spite of the fact that formal concept techniques have been used ..."
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We review a method of generating logical rules, or axioms, from empirical data. This method, using closed set properties of formal concept analysis, has been previously described and tested on rather large sets of deterministic data. In spite of the fact that formal concept techniques have been used to prune frequent set data mining results, frequency and/or statistical significance are totally irrelevant to this method. It is strictly logical and deterministic. The contribution of this paper is a completely new extension of this method to create implications involving numeric inequalities. That is, numerical inequalities such as “age> 39” can be treated as logical predicates that have been extracted from the data itself and not postulated apriori.
Representing Numeric Values in Concept Lattices
"... Abstract. Formal Concept Analysis is based on the occurrence of symbolic attributes in individual objects, or observations. But, when the attribute is numeric, treatment has been awkward. In this paper, we show how one can derive logical implications in which the atoms can be not only boolean symbol ..."
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Abstract. Formal Concept Analysis is based on the occurrence of symbolic attributes in individual objects, or observations. But, when the attribute is numeric, treatment has been awkward. In this paper, we show how one can derive logical implications in which the atoms can be not only boolean symbolic attributes, but also ordinal inequalities, such as x ≤ 9. This extension to ordinal values is new. It employs the fact that orderings are antimatroid closure spaces. 1 Extending Formal Concept Analysis Formal Concept Analysis (FCA), which was initially developed by Rudolf Wille and Bernhard Ganter [3], provides a superb way of describing “concepts”, that is closed sets of attributes, or properties, within a context of occurrences, or objects. One can regard the concept as a closed set of objects with common attributes. Frequently clusters of these concepts, together with their structure, stand out with vivid clarity. However, two unresolved problems are often encountered. First, when concept lattices become large, it is hard to discern or describe significant clusters of related concepts. Gregor Snelting used formal concept analysis to analyze legacy code [6, 14]. 1 Snelting’s goal was to reconstruct the overall system structure by determining which variables (attributes or columns)
Logical Implication and Causal Dependency
"... Abstract. Suppose that whenever event x occurs, a second event y must subsequently occur. We say that x “causes ” y, or y is causally dependent on x. Deterministic causality abounds in software where execution of one routine can necessarily force execution of a subsequent subroutine. Discovery of su ..."
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Abstract. Suppose that whenever event x occurs, a second event y must subsequently occur. We say that x “causes ” y, or y is causally dependent on x. Deterministic causality abounds in software where execution of one routine can necessarily force execution of a subsequent subroutine. Discovery of such causal dependencies can be an important step to understanding the structure of undocumented, legacy code. In this paper we describe a methodology based on formal concept analysis that first uncovers necessary logical implications between software events, and then extracts possible causal dependencies from execution trace streams. We provide an example of its potential by applying our method to 1,227 threads involving 498,489 executed events that were monitored in a wellknown open source middleware system. 1
A review of associative classification mining Original Citation
"... The University Repository is a digital collection of the research output of the University, available on Open Access. Copyright and Moral Rights for the items on this site are retained by the individual author and/or other copyright owners. Users may access full items free of charge; copies of full ..."
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The University Repository is a digital collection of the research output of the University, available on Open Access. Copyright and Moral Rights for the items on this site are retained by the individual author and/or other copyright owners. Users may access full items free of charge; copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational or notforprofit purposes without prior permission or charge, provided: • The authors, title and full bibliographic details is credited in any copy; • A hyperlink and/or URL is included for the original metadata page; and • The content is not changed in any way. For more information, including our policy and submission procedure, please
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"... What Constitutes a Scientific Database? We propose that a scientific database should be inherently different from, say a business database. The difference is based on the nature of science itself, in which hypotheses, or logical implications, form an essential part of the discipline. Empirical obser ..."
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What Constitutes a Scientific Database? We propose that a scientific database should be inherently different from, say a business database. The difference is based on the nature of science itself, in which hypotheses, or logical implications, form an essential part of the discipline. Empirical observations give rise to tentative hypotheses. Individual hypotheses are then tested, refuted or refined, by further empirical observation. In the paper, we propose representing the observational data of science in a lattice format that also conveys all the logical implications that can be supported by those observations. We claim that such a structure can be incrementally created and that the hypotheses formed will adapt to new data. We demonstrate its practicality by presenting two real situations in which it has been used. Finally, we look at the rather considerable storage costs associated with this approach and discuss other limitations that are still unresolved in this new approach to the representation of scientific data. 1
Transformations of Discrete Closure Systems
, 2012
"... Discrete systems such as sets, monoids, groups are familiar categories. The internal structure of the latter two is defined by an algebraic operator. In this paper we concentrate on discrete systems that are characterized by unary operators; these include choice operators σ, encountered in economics ..."
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Discrete systems such as sets, monoids, groups are familiar categories. The internal structure of the latter two is defined by an algebraic operator. In this paper we concentrate on discrete systems that are characterized by unary operators; these include choice operators σ, encountered in economics and social theory, and closure operators ϕ, encountered in discrete geometry and data mining. Because, for many arbitrary operators α, it is easy to induce a closure structure on the base set, closure operators play a central role in discrete systems. Our primary interest is in functions f that map power sets 2U into power sets 2U ′, which are called transformations. Functions over continuous domains are usually characterized in terms of open sets. When the domains are discrete, closed sets seem more appropriate. In particular, we consider monotone transformations which are “continuous”, or “closed”. These can be used to establish criteria for asserting that “the closure of a transformed image under f is equal to the transformed image of the closure”. Finally, we show that the categories MCont and MClo of closure systems with morphisms given by the monotone continuous transformations and monotone closed transformations respectively have concrete direct products. And the supercategory Clo of MClo whose morphisms are just the closed transformations is shown to be cartesian closed.
C1: Y ⊆ Y.ϕ, C2: Y ⊆ Z implies Y.ϕ ⊂ Z.ϕ, and
"... Abstract. We present a model of causality which is defined by the intersection of two distinct closure systems, I and T. To present empirical evidence to demonstrate that this model has practical validity we then examine computer trace data to reveal causal dependencies between individual code modul ..."
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Abstract. We present a model of causality which is defined by the intersection of two distinct closure systems, I and T. To present empirical evidence to demonstrate that this model has practical validity we then examine computer trace data to reveal causal dependencies between individual code modules. From over 498,000 events in an open source system, we tease our 66 apparent causal dependencies. Finally, we explore how to mathematically model the transformation of the causal topology resulting from unfolding events.