In SIGPLAN Notices (December 1992), Dick Wexelblat, the editor, called the debate "the Battle of Berlin". It started in August 1989, when Peter Bollmann and Horst Zuse published the following paper on the application of measurement theory to software metrics:
Zuse, Horst; Bollmann, Peter: Software Metrics - Using Measurement Theory to Describe the Properties and Scales of Static Software Complexity Metrics, SIGPLAN Notices 24, No. 8, New York 1989, 23-33. ACM online.
This is a slightly modified version of the following paper:
Bollmann, Peter; Zuse, Horst: An Axiomatic Approach to Software Complexity Measures. In: J. Rasmussen, P. Zunde (Eds.), Empirical Foundations of Information and Software Science III, Plenum Press, New York 1987, 13-20.
I criticized the paper in SIGPLAN Notices:
Konrad, Erhard: Software Metrics, Measurement Theory, and Viewpoints - Critical Remarks on a New Approach, ACM SIGPLAN Notices 26, No. 3, New York 1991, 53-62. ACM online.
"This paper presents a critical discussion of a new approach to software quality assurance. Zuse and Bollmann, the protagonists of this approach, claim that they can offer a methodology for properly selecting and applying software metrics. Their approach incorporates ideas borrowed from measurement theory and information retrieval. In this paper, it is shown that Zuse and Bollmann go astray even under their own premises." (From the text.)
Bollmann and Zuse tried to refute my criticism (ACM online). My response:
Konrad, Erhard: Application of Measurement Theory to Software Metrics - Comments on the Bollmann-Zuse Approach, ACM SIGPLAN Notices 27, No. 12, New York 1992, 13-19. ACM online.
"In this paper, Bollmann and Zuse's reply to a criticism of their approach to software metrics will be examined. As a result it will be shown that they have failed to achieve their goal of refuting this criticism. ... Bollmann and Zuse do not address the main issue of my criticism, namely the bridge between measurement theory and software metrics. Instead they introduce material susceptible to shortcomings and unsubstantiated claims. This suggests that the Bollmann-Zuse approach is a specious line of research in the field of software metrics." (From the text.)
In the same issue of SIGPLAN notices, Bollmann and Zuse reply to my reply (ACM online). They come to the conclusion that their position is incompatible with my position. I agree.
Meanwhile Zuse had published a book. I wrote a review:
Konrad, Erhard: Review of Zuse, Horst: Software Complexity - Measures and Methods, Zentralblatt für Mathematik / Mathematics Abstracts, 731/68.003, Berlin New York 1992. Also: Report 1/92, TU Berlin, January 1992. Online.
"The aim of this book, as outlined by the author in the preface, is ‘to prepare the reader for a detailed study of the methods of application of measurement theory, the definition and use of scales, the description of measures as ordinal or ratio scale, ... and the application of software complexity measurement in practice. The book presents ... a theoretical foundation of the measurement of software complexity, and ... a detailed discussion of more than ninety software complexity measures and their application to software complexity measurement.’ Unfortunately, the reader who approaches this book with high expectations will be disappointed. A careful study reveals grave shortcomings: Measurement theory is misrepresented; the theoretical foundations of software complexity measurement are unsound; the methods for the practical application of software complexity measurement are insufficiently elaborated. The best features of the book are the nearly complete collection of complexity measures and the extensive annotated bibliography." (From the text.)
In response to my book review, Bollmann and Zuse published two reports:
Bollmann-Sdorra, Peter: Reply to: "Erhard Konrad: Review of Zuse, Horst:
Software Complexity - Measures and Methods", Report,TU Berlin, September 1992.
Bollmann-Sdorra, Peter; Zuse, Horst: Supplement (Part I) for
"Software Complexity - Measures and Methods by Horst Zuse", Proofs
of Theorems, Report, TU Berlin, October 1992.
In the first one, the author tries to hyde the weaknesses of Zuse's book by drawing attention to side-issues. In the second one, the authors correct errors, add mathematical definitions, and prove some theorems that are similar to "theorems" presented in the book without proofs. However, the problem whether Zuse's "Modified Extensive Structure" is an extensive measurement structure is not solved. This gap is fatal to the Bollmann-Zuse approach.
In a second book (Zuse, Horst: A Framework of Software Measurement, Berlin 1998), Zuse tries to remove the gap. He offers a proof for the assertion that his axiom system of a "modified extensive structure" is equivalent to a standard axiom system of an extensive measurement structure (cf. Krantz et al. [1971], Roberts [1979]). Yet the proof is incorrect. On page 675, Zuse claims that line 4 implies line 6. This step, however, is obviously a logical blunder (•≥ is equated with •>; definition of •>: a•>b if and only if a•≥b and not(b•≥a)). So he fails to show that the axiom system of the extensive structure implies the strong Archimedean axiom of the "modified extensive structure". - Hence Zuse's work is unfounded, and it is doubtful whether it can be justified.
Conclusion: Bollmann and Zuse still have to go a long way to bridge measurement
theory and software metrics.
References