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Journal Article

Peirce Algebras

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44183

Brink,  Chris
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45401

Schmidt,  Renate A.
Programming Logics, MPI for Informatics, Max Planck Society;

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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.