Peirce Algebras

Brink, C., Britz, K. and Schmidt, R. A. (1994)

Formal Aspects of Computing 6 (3), 339-358. BiBTeX, DOI Link.

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.

Also available as Tech. Rep. MPI-I-92-229, MPI für Informatik, Saarbrücken, Germany (July 1992). DVI, PostScript
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), Algebraic Methodology and Software Technology: Proceedings of AMAST'93. Workshops in Computing Series, Springer, London, 165-168 (1994). DVI, PostScript

Renate A. Schmidt
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