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Universal logic : an anthology : from Paul Hertz to Dov Gabbay
Béziau J., Springer-Verlag, New York, NY, 2012. 428 pp.  Type: Book (978-3-034601-44-3)
Date Reviewed: Jul 9 2012

The quest for common ground in the expression of logical statements--regardless of the given syntax, semantics, or grammar--has taken the best efforts of notable logicians throughout the 20th century. This book gathers a collection of some of the most notable of their works. Its structure is chronological, but it is not merely a book on the history of universal logic. Each major work is discussed by eminent contemporary researchers, providing context on why a particular idea in logic came into existence.

For example, Rougier’s 1941 work on logical pluralism is discussed by Marion, who traces the context of origin of this work to Lewis’ alternative systems of logic, or Carnap’s logical syntax of language, around the mid-1930s. This leads to the question of whether it is possible to lead away from logical monism, and instead embrace the possibility of different logical systems, which, though free, are not arbitrary, since they must comply with the domain of facts to which the research is relevant. Dana Scott’s discussion on completeness and axiomatizability in many-valued logics is tackled by Humberstone, who argues that it is actually a “finitized” version of the multiple-conclusion logics, inspired by the logics of Łukasiewicz. Other major works either discussed or mentioned include those of Russell and Whitehead (from Principia), Gödel, and Dov Gabbay (his 1996 work seeking to combine logical systems, which is relevant for software engineering).

I highly recommend this book to logicians, mathematicians working on provability theory, and software engineers.

Reviewer:  Arturo Ortiz-Tapia Review #: CR140350 (1211-1108)
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