We present a two-sorted algebra, called a *
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 *terminological logics* arising
in knowledge representation have evolved a semantics best described as
a calculus of relations interacting with sets.

And available as Research Report RR 140, Department of Mathematics, Univ. of Cape Town, South Africa (August 1992).

An extended abstract appears in Nivat, M., Rattray, C., Rus, T. and Scollo, G. (eds),

Home | Publications | FM Group | School | Man Univ

Last modified: 03 Jan 11

Copyright © 1996,7,8 Renate A. Schmidt, School of Computer Science, Man Univ, schmidt@cs.man.ac.uk