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Author, Editor(s)

Author(s):

Brink, Chris
Britz, Katarina
Schmidt, Renate A.

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BibTeX cite key*:

BrinkBritzSchmidt94

Title

Title*:

Peirce Algebras

Journal

Journal Title*:

Formal Aspects of Computing

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Language:

English

Publisher

Publisher's
Name:

Springer

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Publisher's
Address:

Berlin, Germany

ISSN:

0934-5043

Vol, No, pp, Date

Volume*:

6

Number:

3

Publishing Date:

April 1994

Pages*:

339-358

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Note, Abstract, ©

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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MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Programming Logics Group

Audience:

experts only

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BibTeX Entry:

@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).},
}


Entry last modified by Christine Kiesel, 03/12/2010
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Editor(s)
Uwe Brahm
Created
01/14/1995 06:53:12 PM
Revisions
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Editor(s)
Christine Kiesel
Uwe Brahm
Christine Kiesel/AG2/MPII/DE
Christine Kiesel/AG2/MPII/DE
Christine Kiesel/AG2/MPII/DE
Edit Dates
28.08.2001 16:56:06
18.04.97 13:24:14
23/01/96 13:44:18
13/12/95 12:16:45
31.03.95 10:31:02