Algebras of relations of various ranks, some current trends and
applications
H. Andréka, J. X. Madarász and István
Németi
Here the emphasis is on the main pillars of Tarskian structuralist
approach to logic: relation algebras, cylindric algebras, polyadic
algebras, and Boolean algebras with operators. We also tried to
highlight the recent renaissance of these areas and their fusion with
new trends related to logic, like the guarded fragment or dynamic
logic. Tarskian algebraic logic is far too broad and too fruitful and
prolific by now to be covered in a short paper like this. Therefore the
overview part of the
paper is rather incomplete, we had to omit important directions as well
as important results. Hopefully, this incompleteness will be alleviated
by the accompanying paper of Tarek Sayed Ahmed.
Journal on Relation Methods in Computer Science, Vol. 2, pp. 27-49, 2004