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Journal Article

#### Peirce Algebras

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##### Citation

Brink, C., Britz, K., & Schmidt, R. A. (1994). Peirce Algebras.*
Formal Aspects of Computing,* *6*(3), 339-358.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-AD94-D

##### 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.