## Peirce Algebras (1992)

Citations: | 25 - 10 self |

### BibTeX

@MISC{Brink92peircealgebras,

author = {Chris Brink and Katarina Britz and Renate A. Schmidt},

title = {Peirce Algebras},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 relationforming 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 terminological logics arising in knowledge representation have evolved a semantics best described as a calculus of relations interacting with sets.