Relational Methods in Computer Science

1. Front Matter

   Pages i-xv

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2. Background Material

   • Peter Jipsen, Chris Brink, Gunther Schmidt

   Pages 1-21

3. Relation Algebras

   • Roger D. Maddux

   Pages 22-38

4. Heterogeneous Relation Algebra

   • Gunther Schmidt, Claudia Hattensperger, Michael Winter

   Pages 39-53

5. Fork Algebras

   • Armando Haeberer, Marcelo Frias, Gabriel Baum, Paulo Veloso

   Pages 54-69

6. Relation Algebra and Modal Logics

   • Holger Schlingloff, Wolfgang Heinle

   Pages 70-89

7. Relational Formalisation of Nonclassical Logics

   • Ewa Orlowska

   Pages 90-105

8. Linear Logic

   • Jules Desharnais, Bernard Hodgson, John Mullins

   Pages 106-114

9. Relational Semantics of Functional Programs

   • Rudolf Berghammer, Burghard von Karger

   Pages 115-130

10. Algorithms from Relational Specifications

    • Rudolf Berghammer, Burghard von Karger

    Pages 131-149

11. Programs and Datatypes

    • Henk Doornbos, Netty van Gasteren, Roland Backhouse

    Pages 150-165

12. Refinement and Demonic Semantics

    • Jules Desharnais, Ali Mili, Thanh Tung Nguyen

    Pages 166-183

13. Tabular Representations in Relational Documents

    • Ryszard Janicki, David Lorge Parnas, Jeffery Zucker

    Pages 184-196

14. Databases

    • Ali Jaoua, Nadir Belkhiter, Habib Ounalli, Théodore Moukam

    Pages 197-210

15. Logic, Language, and Information

    • Patrick Blackburn, Maarten de Rijke, Yde Venema

    Pages 211-225

16. Natural Language

    • Michael Böttner

    Pages 226-246

17. Back Matter

    Pages 247-275

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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).

• algebra
• algorithm
• algorithms
• calculus
• computer
• computer science
• database
• databases
• development
• language
• logic
• relational database
• semantics
• software

• Department of Mathematics and Applied Mathematics, University of Cape Town, Cape Town, South Africa

  Chris Brink

• Fakultät für Informatik, Universität der Bundeswehr München, Neubiberg, Federal Republic of Germany

  Wolfram Kahl, Gunther Schmidt

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