Jacques Riguet

Jacques Riguet (1921 to October 20, 2013) was a French mathematician known for his contributions to algebraic logic and category theory. According to Gunther Schmidt and Thomas Ströhlein, "Alfred Tarski and Jacques Riguet founded the modern "calculus of relations".[1]

Career

Already at his lycée, Riguet was impressed by the power of geometric reasoning. He studied Louis Couturat and Bourbaki, who made contributions to logic and set theory.[2] Riguet studied higher mathematics with Albert Châtelet and was introduced to lattices. In 1948 he published "Relations binaires, fermetures, correspondances de Galois"[3] which revived the calculus of binary relations.

He published his thesis Fondements de la Theorie de Relations Binaires in October 1951. In 1954 Riguet gave a plenary address at the International Congress of Mathematicians in Amsterdam, speaking on the applications of binary relations to algebra and machine theory. For a time, Riguet attended the seminary of Jacques Lacan.

Riguet was employed at Centre national de la recherche scientifique until 1957.[2]

Relations

In Riguet's work the composition of relations is the basis for characterizing relations, replacing the element-wise descriptions that use logical formulations. For example, he described the Schröder rules. His work was reviewed in Journal of Symbolic Logic by Øystein Ore.[4]

Some of Riguet’s contributions can be described using structure of the logical matrix associated with a relation. If u and v are logical vectors, then their logical outer product produces the associated logical matrix Riguet calls the associated relation a rectangular relation, and if it happens to be symmetric it is a square relation.[5]

In 1950 he submitted "Sur les ensembles reguliers de relations binaires",[6] and an article on difunctional relations, those with logical matrix in a block diagonal form.[7] The following year he provided an algebraic characterization of relations with a logical matrix in a block echelon form which were associated with Norman Macleod Ferrers.[8]

In 1954 Riguet described the extension of the calculus of binary relations to a calculus of Boolean matrices.[9][10]

Category theory

In 1958 Riguet went to Zurich, working with IBM , studying category theory. He published the following papers on that topic:

  • 1962: "Programmation et theorie des categories", in Proceedings of Symposium on Symbolic Languages and Data Processing, Rome (1961), pp 88–98, Gordon & Breach
  • 1973: "Probabilites et theorie de la decision du point de vue de la theorie des categories" (Amiens colloquium) Cahiers de Topologie et Géométrie Différentielle Catégoriques 14(2)
  • 1975 : "Theorie des jeux et funciones de Grundy du point de vue de la theorie des categories" (TAC-Chantilly) Cahiers de Topologie et Géométrie Différentielle Catégoriques 16(4) : 441
  • 1989 : "Galois correspondences in category theory", Hesselberg-Combinatorics
  • 1992: (with Rene Guitart) Enveloppe Karoubienne et categorie de Kleisli, Cahiers de Topologie et Géométrie Différentielle Catégoriques 33(3) : 261–6, via Numdam.org

Riguet participated in the Séminaire Itinérant des Catégories.[11]

References

  1. ↑ Schmidt, Gunther; Ströhlein, Thomas (6 December 2012). Relations and Graphs: Discrete Mathematics for Computer Scientists. Springer Science & Business Media. p. 277. ISBN 978-3-642-77968-8.
  2. 1 2 Stephane Dugowson and others Hommage a Jacques Riguet at Google Sites
  3. ↑ Bulletin de la Société Mathématique de France 76: 114–55
  4. ↑ Journal of Symbolic Logic 16(1): 61
  5. ↑ Gunther Schmidt (2013). Relational Mathematics. Cambridge University Press. p. 95. doi:10.1017/CBO9780511778810. ISBN 9780511778810.
  6. ↑ Comptes Rendus 231: 936,7
  7. ↑ J. Riguet (1950) "Quelques proprietes des relations difonctionelles", Comptes Rendus 230: 1999–2000
  8. ↑ "Les relations de Ferrers", Comptes Rendus 232: 1729,30
  9. ↑ J. Riguet (1954) "Sur l’extension du calcul du relations binaries au calcul des matrices du algebra de Bool complete", Comptes Rendus 238: 2382–5
  10. ↑ Roland Fraisse (1956) Review of Riguet's extension of calculus of relations, Journal of Symbolic Logic 21(4): 397,8 via Project Euclid
  11. ↑ Séminaire Itinérant des Catégories (16 November 2013) Hommage du SIC a Jacques Riguet
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