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  Peirce Algebras

Brink, C., Britz, K., & Schmidt, R. A. (1994). Peirce Algebras. Formal Aspects of Computing, 6(3), 339-358.

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 Creators:
Brink, Chris1, Author           
Britz, Katarina, Author
Schmidt, Renate A.1, Author           
Affiliations:
1Programming Logics, MPI for Informatics, Max Planck Society, ou_40045              

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 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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Language(s): eng - English
 Dates: 2010-03-121994
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: eDoc: 519512
Other: Local-ID: C1256104005ECAFC-4DE8627844A8058EC125614400624166-BrinkBritzSchmidt94
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Title: Formal Aspects of Computing
Source Genre: Journal
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Pages: - Volume / Issue: 6 (3) Sequence Number: - Start / End Page: 339 - 358 Identifier: ISSN: 0934-5043