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Peirce algebras

Authors:

Katarina Britz,

Renate A. SchmidtAuthors Info & Claims

Formal Aspects of Computing, Volume 6, Issue 3

Pages 339 - 358

https://doi.org/10.1007/BF01215410

Published: 01 May 1994 Publication History

Abstract

We present a two-sorted algebra, called aPeirce 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-calledterminological logics arising in knowledge representation have evolved a semantics best described as a calculus of relations interacting with sets.

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Cited By

Pagliani P(2021)A Framework for the Approximation of RelationsIntelligence Science III10.1007/978-3-030-74826-5_5(49-65)Online publication date: 15-Apr-2021
https://doi.org/10.1007/978-3-030-74826-5_5
Staker R(2014)5.2.1 Systems Engineering and the Semantic WebINCOSE International Symposium10.1002/j.2334-5837.2003.tb02617.x13:1(289-300)Online publication date: 4-Nov-2014
https://doi.org/10.1002/j.2334-5837.2003.tb02617.x
Schmidt RHustadt U(2013)First-Order Resolution Methods for Modal LogicsProgramming Logics10.1007/978-3-642-37651-1_15(345-391)Online publication date: 2013
https://doi.org/10.1007/978-3-642-37651-1_15
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Index Terms

Peirce algebras
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
  2. Symbolic and algebraic manipulation
2. Theory of computation

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Formal Aspects of Computing

Formal Aspects of Computing Volume 6, Issue 3

May 1994

112 pages

ISSN:0934-5043

EISSN:1433-299X

Issue’s Table of Contents

© BCS 1994.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 May 1994

Accepted: 15 April 1993

Received: 15 March 1992

Published in FAC Volume 6, Issue 3

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Cited By

Pagliani P(2021)A Framework for the Approximation of RelationsIntelligence Science III10.1007/978-3-030-74826-5_5(49-65)Online publication date: 15-Apr-2021
https://doi.org/10.1007/978-3-030-74826-5_5
Staker R(2014)5.2.1 Systems Engineering and the Semantic WebINCOSE International Symposium10.1002/j.2334-5837.2003.tb02617.x13:1(289-300)Online publication date: 4-Nov-2014
https://doi.org/10.1002/j.2334-5837.2003.tb02617.x
Schmidt RHustadt U(2013)First-Order Resolution Methods for Modal LogicsProgramming Logics10.1007/978-3-642-37651-1_15(345-391)Online publication date: 2013
https://doi.org/10.1007/978-3-642-37651-1_15
Fischer Nilsson J(2013)Diagrammatic Reasoning with Classes and RelationshipsVisual Reasoning with Diagrams10.1007/978-3-0348-0600-8_6(83-100)Online publication date: 2013
https://doi.org/10.1007/978-3-0348-0600-8_6
Fernando T(2011)Regular relations for temporal propositionsNatural Language Engineering10.1017/S135132491100009X17:2(163-184)Online publication date: 1-Apr-2011
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Fischer Nilsson J(2011)Querying Class-Relationship Logic in a Metalogic FrameworkFlexible Query Answering Systems10.1007/978-3-642-24764-4_9(96-107)Online publication date: 2011
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Schmidt R(2011)Synthesising Terminating Tableau Calculi for Relational LogicsRelational and Algebraic Methods in Computer Science10.1007/978-3-642-21070-9_3(40-49)Online publication date: 2011
https://doi.org/10.1007/978-3-642-21070-9_3
Pinto SOliveira‐Martins M(2011)Congruences and ideals on Boolean modulesMathematical Logic Quarterly10.1002/malq.20102005757:6(571-581)Online publication date: 4-Oct-2011
Szymczak B(2009)Ontological semantics in modified categorial grammar2009 International Multiconference on Computer Science and Information Technology10.1109/IMCSIT.2009.5352712(295-298)Online publication date: Oct-2009
https://doi.org/10.1109/IMCSIT.2009.5352712
Schmidt R(2009)A new methodology for developing deduction methodsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-009-9155-455:1-2(155-187)Online publication date: 1-Feb-2009
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