@ARTICLE{BrinkBritzSchmidt94,
AUTHOR = {Brink, C. and Britz, K. and Schmidt, R. A.},
YEAR = {1994},
TITLE = {Peirce Algebras},
JOURNAL = {Formal Aspects of Computing},
VOLUME = {6},
NUMBER = {3},
PAGES = {339--358},
NOTE = {Also available as Technical Report MPI-I-92-229,
Max-Planck-Institut f{\"u}r Informatik, Saarbr{\"u}cken, Germany (July
1992), and as Research Report RR 140, Department of Mathematics,
University of Cape Town, Cape Town, South Africa (August 1992). An
extended abstract appears in Nivat, M., Rattray, C., Rus, T. and
Scollo, G. (eds), {\em Algebraic Methodology and Software Technology
(AMAST'93): Proceedings of the Third International Conference on
Algebraic Methodology and Software Technology}. {\em Workshops in
Computing} Series, Springer, London, 165--168 (1994).},
ABSTRACT = {We present a two-sorted algebra, called a {\em Peirce
algebra}, of relations and sets interacting with each other. In a
Peirce algebra, sets can combine with each other as in a Boolean
algebra, relations can combine with each other as in a relation algebra,
and in addition we have both a set-forming operator on relations (the
Peirce product of Boolean modules) and a relation-forming operator on
sets (a cylindrification operation). Two applications of Peirce algebras
are given. The first points out that Peirce algebras provide a natural
algebraic framework for modelling certain programming constructs. The
second shows that the so-called {\em terminological logics} arising in
knowledge representation have evolved a semantics best described as a
calculus of relations interacting with sets.}
URL = {http://www.cs.man.ac.uk/~schmidt/publications/BrinkBritzSchmidt94.html},
}