@ARTICLE{Schmidt94a,
AUTHOR = {Schmidt, R. A.}, 
MONTH = {April},
YEAR = {1994},
TITLE = {Peirce Algebras and Their Applications in Artificial
Intelligence and Computational Linguistics: Abstract},
JOURNAL = {SIGALA Newsletter},
VOLUME = {2},
NUMBER = {1},
PAGES = {27},
NOTE = {Abstract of a talk held at the Dagstuhl Seminar on Relational
Methods in Computer Science, Dagstuhl, Germany (January 1994).  Also in
Brink, C. and Schmidt, G. (eds) (1994), Relational Methods in Computer
Science, Dagstuhl-Seminar-Report 80 (9403), IBFI, Schlo{\ss} Dagstuhl,
Wadern, Germany, 21--22.},
ABSTRACT = {In [1] 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).  Peirce algebras provide useful
formalisations for various fields in Computer Science.   In this talk I
focus on the application of Peirce algebras in artificial intelligence
and computational intelligence.  In particular, I show that the
so-called {\em terminological logics} arising in knowledge
representation (originating with a system called {\sc kl-one}) have
evolved a semantics best described as a calculus of relations
interacting with sets [1,2,3].  In computational linguistics P. Suppes
(1976,1979,1981) and M. B\"ottner (1992) use concrete Peirce algebras as
a relational formalisation of the semantics of the English language.  In
[4] I link both these applications and show that Peirce algebra provides
a useful bridge for utilising the linguistic investigations for the
problem of finding adequate terminological representations for given
information formulated in ordinary English.
\bibliographystyle{plain}
\def\refname{\normalsize \bf References}
\begin{thebibliography}{[9]}
\bibitem{}
Brink, C., Britz, K. and Schmidt, R.~A. (1994),
  Peirce Algebras.
  {\em Formal Aspects of Computing} {\bf 6}(3),~339-358.
\bibitem{}
Brink, C. and Schmidt, R.~A. (1992),
  Subsumption Computed Algebraically.
  {\em Computers and Mathematics with Applications} {\bf 23}(2--5),~329--342.
\bibitem{}
Schmidt, R.~A. (1991),
  Algebraic Terminological Representation.
  Master's Thesis, University of Cape Town.
\bibitem{}
Schmidt, R.~A. (1993),
  Terminological Representation, Natural Language \& Relation Algebra.
  In the {\em Proceedings GWAI-92}, Vol. 671 of {\em LNAI}, 
  357--371.
\end{thebibliography}
}
URL = {http://www.cs.man.ac.uk/~schmidt/publications/dagstuhl94.dvi.gz, http://www.cs.man.ac.uk/~schmidt/publications/dagstuhl94.ps.gz},
}