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The genesis of Boole’s logic. Its history and a computer exploration. (English) Zbl 1183.03003

Memorias de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid. Serie de Ciencias Exactas 33. Madrid: Real Academia de Ciencias Exactas, Físicas y Naturales (ISBN 978-84-87125-44-7/pbk). xi, 154 p. (2005).
The book under review has a double character, linking history of logic and computer science – it deals with historical aspects (Chapters 2, 3 and 7) and the computational aspects (Chapters 4, 5 and 6) related to the genesis of Boole’s logic. Chapter 2 presents a biography of Boole. As the authors mention, it is not exhaustive. Its aim is to throw some light on the issues considered in the chapters that follow. Chapter 3 deals with the controversy about the quantification of predicates between A. De Morgan and W. Hamilton. This controversy made Boole decide to work out and publish his The mathematical analysis of logic. The next three chapters deal with computational aspects of Boole’s systems. In Chapter 4, the influence of Boole’s work in a method called “the method of separation of symbols” on the making of his logic is considered. It is claimed that, although Boole was influenced by D. F. Gregory, he had arrived at almost the same methodology by himself. The topic of an essential part of Chapter 4 is the computer algebra approach to Boole’s inference procedures relating these procedures to a recent result that links logical consequence with an ideal membership problem in a polynomial ring. In Chapter 5, it is shown how this result can be applied to verification and extraction of consequences in rule-based expert systems. Three such systems are described as an illustration. In Chapter 6, Boole’s discovery of logic is approached from a computational viewpoint by building a program (BOOLE2) that emulates the process that Boole pursued to build his logic. In the last Chapter 7, the authors return to the historical problems by examining how “extrascientific” facts may have influenced the logical ideas of Boole, in particular the authors consider claims of Mary Everest, Boole’s wife, in this respect.
The book is an interesting study of Boole’s logical ideas both from the historical as well as computer-scientific point of view. Considering modern computational achievements, the authors show the significance of Boole’s logic and its applications.

MSC:

03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
01A55 History of mathematics in the 19th century
01A70 Biographies, obituaries, personalia, bibliographies
03-03 History of mathematical logic and foundations
03-04 Software, source code, etc. for problems pertaining to mathematical logic and foundations
68-03 History of computer science
68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
68U20 Simulation (MSC2010)
68W30 Symbolic computation and algebraic computation

Biographic References:

Boole, George
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