Jacques Riguet (1921 to October 20, 2013) was a French mathematician known for his contributions to
algebraic logic
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with Free variables and bound variables, free variables.
What is now usually called classical algebraic logic focuses on the identification and algebraic de ...
and
category theory
Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory ...
. According to
Gunther Schmidt
Gunther Schmidt (born 1939, Rüdersdorf) is a Germans, German mathematician who works also in informatics.
Life
Schmidt began studying Mathematics in 1957 at Göttingen University. His academic teachers were in particular Kurt Reidemeister, W ...
and Thomas Ströhlein, "
Alfred Tarski
Alfred Tarski (; ; born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician ...
and Jacques Riguet founded the modern
calculus of relations
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables.
What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for ...
".
Career
Already at his lycée, Riguet was impressed by the power of logical reasoning in geometry. He studied
Louis Couturat
Louis Couturat (; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido.
Life and education
Born in Paris. In 1887 he entered École Normale S ...
and
Bourbaki Bourbaki(s) may refer to :
Persons and science
* Charles-Denis Bourbaki (1816–1897), French general, son of Constantin Denis Bourbaki
* Colonel Constantin Denis Bourbaki (1787–1827), officer in the Greek War of Independence and serving in the ...
, who made contributions to logic and
set theory
Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...
.
[Stephane Dugowson and others]
Hommage a Jacques Riguet
at Google Sites
Google Sites is a structured wiki and web page creation tool included as part of the free, web-based Google Docs Editors suite offered by Google. The service includes Google Docs, Google Sheets, Google Slides, Google Drawings, Google For ...
Riguet studied higher mathematics with
Albert Châtelet
Albert Châtelet (24 October 1883 – 30 June 1960) was a French politician and mathematician.
Biography
Châtelet was a student at the École normale supérieure (Paris) from 1905 to 1908, succeeding to the Agrégation (a highly selective comp ...
and was introduced to
lattice
Lattice may refer to:
Arts and design
* Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material
* Lattice (music), an organized grid model of pitch ratios
* Lattice (pastry), an or ...
s. In 1948 he published "Relations binaires, fermetures, correspondances de Galois" which revived the calculus of
binary relation
In mathematics, a binary relation associates some elements of one Set (mathematics), set called the ''domain'' with some elements of another set called the ''codomain''. Precisely, a binary relation over sets X and Y is a set of ordered pairs ...
s.
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
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...
in Amsterdam, speaking on the applications of binary relations to algebra and machine theory. For a time, Riguet attended the seminary of
Jacques Lacan
Jacques Marie Émile Lacan (, ; ; 13 April 1901 – 9 September 1981) was a French psychoanalyst and psychiatrist. Described as "the most controversial psycho-analyst since Sigmund Freud, Freud", Lacan gave The Seminars of Jacques Lacan, year ...
.
Riguet was employed at
Centre national de la recherche scientifique
The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe.
In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...
until 1957.
[
]
Relations
In Riguet's work the composition of relations
In the mathematics of binary relations, the composition of relations is the forming of a new binary relation from two given binary relations ''R'' and ''S''. In the calculus of relations, the composition of relations is called relative multiplica ...
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
The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by '' Mathematical Reviews'', Zent ...
by Øystein Ore
Øystein Ore (7 October 1899 – 13 August 1968) was a Norwegian mathematician known for his work in ring theory, Galois connections, graph theory, and the history of mathematics.
Life
Ore graduated from the University of Oslo in 1922, with a ...
.
Some of Riguet’s contributions can be described using structure of the logical matrix
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets. It is an important tool in ...
associated with a relation. If ''u'' and ''v'' are logical vectors, then their logical outer product
In linear algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. If the two coordinate vectors have dimensions ''n'' and ''m'', the ...
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.
In 1950 he submitted "Sur les ensembles reguliers de relations binaires", and an article on difunctional relations, those with logical matrix in a block diagonal
In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices.
Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix w ...
form.
The following year he provided an algebraic characterization of heterogeneous relation
In mathematics, a binary relation associates some elements of one set called the ''domain'' with some elements of another set called the ''codomain''. Precisely, a binary relation over sets X and Y is a set of ordered pairs (x, y), where x i ...
s with a logical matrix comparable to a Ferrers diagram
In number theory and combinatorics, a partition of a non-negative integer , also called an integer partition, is a way of writing as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same ...
. Since Ferrers diagrams order the partitions of an integer, Riguet extended order theory beyond relations restricted to one set.
In 1954 Riguet described the extension of the calculus of binary relations to a calculus of Boolean matrices.
Category theory
In 1958 Riguet went to Zurich, working with IBM
International Business Machines Corporation (using the trademark IBM), nicknamed Big Blue, is an American Multinational corporation, multinational technology company headquartered in Armonk, New York, and present in over 175 countries. It is ...
, studying category theory
Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. 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
Taylor & Francis Group is an international company originating in the United Kingdom that publishes books and academic journals. Its parts include Taylor & Francis, CRC Press, Routledge, F1000 Research and Dovepress. It is a division of In ...
* 1973: "Probabilites et theorie de la decision du point de vue de la theorie des categories" (Amiens colloquium) 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.[Séminaire Itinérant des Catégories (16 November 2013]
Hommage du SIC a Jacques Riguet
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References
{{DEFAULTSORT:Riguet, Jacques
1921 births
2013 deaths
20th-century French mathematicians
Category theorists