MPI-I-92-229
Peirce algebras
Brink, Chris and Britz, Katarina and Schmidt, Renate A.
July 1992, 22 pages.
.
Status: available - back from printing
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.
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MPI-I-92-229.pdf
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URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1992-229
BibTeX
@TECHREPORT{BrinkBritzSchmidt92,
AUTHOR = {Brink, Chris and Britz, Katarina and Schmidt, Renate A.},
TITLE = {Peirce algebras},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
NUMBER = {MPI-I-92-229},
MONTH = {July},
YEAR = {1992},
ISSN = {0946-011X},
}