Note: |
Also available as Research Report MPI-I-92-229, Max-Planck-Institut für Informatik, Saarbrücken, Germany (July 1992), and as Research Report RR 140, Department of Mathematics, University of Cape Town, Cape Town, South Africa (August 1992). An extended abstract appears in Nivat, M., Rattray, C., Rus, T. and Scollo, G. (eds), {\em Algebraic Methodology and Software Technology (AMAST'93): Proceedings of the 3rd International Conference on Algebraic Methodology and Software Technology}. {\em Workshops in Computing} Series, Springer-Verlag, London, 165-168 (1994). |
(LaTeX) 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. |
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@ARTICLE{BrinkBritzSchmidt94,
AUTHOR = {Brink, Chris and Britz, Katarina and Schmidt, Renate A.},
TITLE = {Peirce Algebras},
JOURNAL = {Formal Aspects of Computing},
PUBLISHER = {Springer},
YEAR = {1994},
NUMBER = {3},
VOLUME = {6},
PAGES = {339--358},
ADDRESS = {Berlin, Germany},
MONTH = {April},
ISBN = {0934-5043},
NOTE = {Also available as Research Report MPI-I-92-229, Max-Planck-Institut für Informatik, Saarbrücken, Germany (July 1992), and as Research Report RR 140, Department of Mathematics, University of Cape Town, Cape Town, South Africa (August 1992). An extended abstract appears in Nivat, M., Rattray, C., Rus, T. and Scollo, G. (eds) , {\em Algebraic Methodology and Software Technology (AMAST'93): Proceedings of the 3rd International Conference on Algebraic Methodology and Software Technology}. {\em Workshops in Computing} Series, Springer-Verlag, London, 165-168 (1994).},
}
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Uwe Brahm | Created
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Christine Kiesel/AG2/MPII/DE | Edit Dates
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