Comparing Two Different Approaches to Products in Abstract Relation Algebra

During the development of relation algebra as a formal programming tool, the need of some form of “categorical product” of relations became apparent, whether as a type or as an operation. Two approaches arose in the late 70’s and the early 80’s which will be referred here as the “Munich approach” (see, e.g., [18, 7]) and the “Rio approach” (see, e.g., [13, 12, 22]).

[1]  Gunther Schmidt,et al.  Relations and Graphs: Discrete Mathematics for Computer Scientists , 1993 .

[2]  Gunther Schmidt,et al.  Relation algebras: Concept of points and representability , 1985, Discret. Math..

[3]  Willem P. de Roever,et al.  Recursive program schemes: semantics and proof theory , 1976, Mathematical Centre Tracts.

[4]  A. Tarski,et al.  A Formalization Of Set Theory Without Variables , 1987 .

[5]  A. Tarski,et al.  Boolean Algebras with Operators , 1952 .

[6]  Hans Zierer,et al.  Relation Algebraic Domain Constructions , 1991, Theor. Comput. Sci..

[7]  Gunther Schmidt,et al.  The RELVIEW-System , 1991, STACS.

[8]  Alfred Tarski,et al.  Relational selves as self-affirmational resources , 2008 .

[9]  Gunther Schmidt,et al.  Symmetric Quotients and Domain Constructions , 1989, Inf. Process. Lett..

[10]  C. J. Everett,et al.  Projective Algebra I , 1946 .

[11]  Alfred Tarski,et al.  Distributive and Modular Laws in the Arithmetic of Relation Algebras , 1953 .

[12]  Gunther Schmidt,et al.  Programs as Partial Graphs I: Flow Equivalence and Correctness , 1981, Theor. Comput. Sci..

[13]  Alexander R. Bednarek,et al.  Projective algebra and the calculus of relations , 1978, Journal of Symbolic Logic.

[14]  Paulo A. S. Veloso,et al.  A finitary relational algebra for classical first-order logic , 1991 .

[15]  Rudolf Berghammer,et al.  Relational Algebraic Semantics of Deterministic and Nondeterministic Programs , 1986, Theor. Comput. Sci..