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Peirce algebras

MPG-Autoren
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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Volltexte (frei zugänglich)

MPI-I-92-229.pdf
(beliebiger Volltext), 138KB

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Zitation

Brink, C., Britz, K., & Schmidt, R. A.(1992). Peirce algebras (MPI-I-92-229). Saarbrücken: Max-Planck-Institut für Informatik.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0014-B1DF-C
Zusammenfassung
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 relation-forming 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 {\em terminological logics} arising in knowledge representation have evolved a semantics best described as a calculus of relations interacting with sets.