Formal Aspects of Computing

, Volume 6, Issue 3, pp 339–358 | Cite as

Peirce algebras

  • Chris Brink
  • Katarina Britz
  • Renate A. Schmidt
Article

Abstract

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

Keywords

Boolean modules Relation algebras Terminological logics Weakest prespecifications 

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Copyright information

© BCS 1994

Authors and Affiliations

  • Chris Brink
    • 1
  • Katarina Britz
    • 1
  • Renate A. Schmidt
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of Cape TownRondeboschSouth Africa
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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