MPI-INF Logo
MPI-INF/SWS Research Reports 1991-2017

2. Number - only D2

MPI-I-92-229

Peirce algebras

Brink, Chris and Britz, Katarina and Schmidt, Renate A.

July 1992, 22 pages.

.
Status: available - back from printing

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 relation-forming operator on sets (the Peirce product of Boolean modules) and a set-forming operator on relations (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.

  • MPI-I-92-229.pdfMPI-I-92-229.pdfMPI-I-92-229.dvi
  • Attachement: MPI-I-92-229.dvi (102 KBytes); MPI-I-92-229.pdf (137 KBytes)

URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1992-229

Hide details for BibTeXBibTeX
@TECHREPORT{BrinkBritzSchmidt92,
  AUTHOR = {Brink, Chris and Britz, Katarina and Schmidt, Renate A.},
  TITLE = {Peirce algebras},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-92-229},
  MONTH = {July},
  YEAR = {1992},
  ISSN = {0946-011X},
}