Peirce algebras (Q1333408)

Since the early eighties, several kinds of relation algebras and their extensions have had wide applications outside pure logic, mainly in computer science. The paper under review falls into the category of publications of this type. Roughly, a Peirce algebra (PA, for short) is a two-sorted algebra consisting of a Boolean algebra of sets, a Tarski relation algebra of relations, and certain mixed type operations: a set- forming operator on relations and a relation-forming operator on sets. The authors give several examples of PAs, do some arithmetic in them and discuss connections between these algebras and such structures as Boolean modules (introduced by the first author in 1981) and dynamic algebras. In the final section of the paper they argue that PAs form a natural algebraic framework for modelling some concepts in the weakest prespecification theory, and show that they also have certain advantages for describing the semantics of the so-called terminological logics (which arise in knowledge representation).