Abstract :
[en] These are the slides of the "IFORS Distinguished Lecture" that I delivered at the INFORMS Annual meeting in November 2011. The title of the lecture is the title of a monograph co-authored by Peter L. Hammer and Sergiu Rudeanu, which appeared in 1968. Their pioneering work has stimulated a large amount of research and has been very frequently cited. Over the last year, the late Peter Hammer and myself have published two distant follow-ups to this classical book: a monograph entitled Boolean Functions: Theory, Algorithms, and Applications (700 pages, Cambridge University Press, 2011), and a collection of survey papers on Boolean Models and Methods in Mathematics, Computer Science and Engineering (780 pages, Cambridge University Press, 2010). The size of these two volumes and of their bibliographic sections are witnesses of the vitality of the field and of its impressive development. Boolean functions are actually among the most fundamental objects investigated in mathematics, and provide the basic building blocks for many models arising in operations research, computer science, artificial intelligence, economics, engineering, cryptography, biology, and other fields of application.
In this lecture, I propose a brief overview of some fundamental Boolean models, I discuss applications in corporate governance (modeling of shareholders’ power) and in classification (Logical Analysis of Data), and I mention a few challenging research problems.
