Overview
- Editors:
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Chris Brink
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Department of Mathematics and Applied Mathematics, University of Cape Town, Cape Town, South Africa
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Wolfram Kahl
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Fakultät für Informatik, Universität der Bundeswehr München, Neubiberg, Federal Republic of Germany
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Gunther Schmidt
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Fakultät für Informatik, Universität der Bundeswehr München, Neubiberg, Federal Republic of Germany
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Table of contents (15 chapters)
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- Peter Jipsen, Chris Brink, Gunther Schmidt
Pages 1-21
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- Gunther Schmidt, Claudia Hattensperger, Michael Winter
Pages 39-53
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- Armando Haeberer, Marcelo Frias, Gabriel Baum, Paulo Veloso
Pages 54-69
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- Holger Schlingloff, Wolfgang Heinle
Pages 70-89
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- Jules Desharnais, Bernard Hodgson, John Mullins
Pages 106-114
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- Rudolf Berghammer, Burghard von Karger
Pages 115-130
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- Rudolf Berghammer, Burghard von Karger
Pages 131-149
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- Henk Doornbos, Netty van Gasteren, Roland Backhouse
Pages 150-165
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- Jules Desharnais, Ali Mili, Thanh Tung Nguyen
Pages 166-183
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- Ryszard Janicki, David Lorge Parnas, Jeffery Zucker
Pages 184-196
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- Ali Jaoua, Nadir Belkhiter, Habib Ounalli, Théodore Moukam
Pages 197-210
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- Patrick Blackburn, Maarten de Rijke, Yde Venema
Pages 211-225
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Back Matter
Pages 247-275
About this book
The calculus of relations has been an important component of the development of logic and algebra since the middle of the nineteenth century, when Augustus De Morgan observed that since a horse is an animal we should be able to infer that the head of a horse is the head of an animal. For this, Aristotelian syllogistic does not suffice: We require relational reasoning. George Boole, in his Mathematical Analysis of Logic of 1847, initiated the treatment of logic as part of mathematics, specifically as part of algebra. Quite the opposite conviction was put forward early this century by Bertrand Russell and Alfred North Whitehead in their Principia Mathematica (1910 - 1913): that mathematics was essentially grounded in logic. Logic thus developed in two streams. On the one hand algebraic logic, in which the calculus of relations played a particularly prominent part, was taken up from Boole by Charles Sanders Peirce, who wished to do for the "calculus of relatives" what Boole had done for the calculus of sets. Peirce's work was in turn taken up by Schroder in his Algebra und Logik der Relative of 1895 (the third part of a massive work on the algebra of logic). Schroder's work, however, lay dormant for more than 40 years, until revived by Alfred Tarski in his seminal paper "On the calculus of binary relations" of 1941 (actually his presidential address to the Association for Symbolic Logic).
