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1. Relation Algebras, 150 - Elsevier
The modern theory of algebras of binary Relations, reformulated by Tarski as an abstract, algebraic, equational theory of Relation algebras,
http://www.elsevier.com/wps/product/cws_home/706796
 Home Site map Elsevier websites Alerts ... Relation Algebras, 150 Book information Product description Audience Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view RELATION ALGEBRAS, 150 To order this title, and for more information, click here By Roger Maddux , Department of Mathematics, Iowa State University, Ames, Iowa, 5001, USA Included in series Studies in Logic and the Foundations of Mathematics, 150 Description The modern theory of algebras of binary relations, reformulated by Tarski as an abstract, algebraic, equational theory of relation algebras, has considerable mathematical significance, with applications in various fields: e.g., in computer science-databases, specification theory, AI-and in anthropology, economics, physics, and philosophical logic. This comprehensive treatment of the theory of relation algebras and the calculus of relations is the first devoted to a systematic development of the subject. Audience Mathematicians, logicians, computer scientists, and philosophers

2. PERA: Package For Extended Relation Algebras
PERA deals with (binary) Relation algebras extended with a neighborhood structure. For a very simple presentation (in french) look at Euzenat 98a.
http://www.inrialpes.fr/exmo/software/pera/
##### PERA: package for extended relation algebras
PERA is a set of files programmed in Maple allowing to use relation algebras extended with a neighborhood structure.
It allows to describe relational algebras, use them (through composition of inverse tests for instance) and manipulate them (through product, weakening or interval composition).
##### The relation algebra structure
PERA deals with (binary) relation algebras extended with a neighborhood structure. For a very simple presentation (in french) look at [ Euzenat 98a ]. For more information, one can consult the Maple worksheet which contains more references.
##### What can be done
A good example of what can be done with PERA is provided in the PERA worksheet . For those non familiar with Maple, the PostScript version of the worksheet is provided here To sum up, PERA allows to:
• Create an extended relation algebra;
• Use it through its operators (composition, inverse, neighborhood, upward and downward granularity);
• Build a new extended relation algebra through product (soon), interval, weakening and restriction;
• Rename the relations of an algebra;

3. RelMiCS10/AKA5 - Main Page
We invite submissions on the general topics of Relation algebra and Kleene Relation algebras and Kleene algebras; related formalisms such as process
http://www.uni-augsburg.de/rel_aka
##### (near Munich), Germany Monday, April 7 - Friday, April 11, 2008 http://www.uni-augsburg.de/rel_aka
Submission is closed
General
Invited Speakers Proceedings Dates ... Contact General
Over the past fifteen years, the RelMiCS meetings have been a main forum for researchers who use the calculus of relations and similar algebraic formalisms as methodological and conceptual tools. The workshop series on Applications of Kleene algebra started with a Dagstuhl seminar in 2001 and has been co-organised with the RelMiCS conference since. Due to their considerable overlap, the two events have a joint PC and joint proceedings. Their scope comprises relation algebra, fixpoint calculi, semiring theory, iteration algebras, process algebras and dynamic algebras. Applications include formal algebraic modelling, the semantics, analysis and development of programs, formal language theory and combinatorial optimisation. We invite submissions on the general topics of Relation algebra and Kleene algebra in computer science. The main focus will lie on formal methods for software engineering, logics of programs and links with neighbouring disciplines. Particular topics of the conference cover, but are not limited to the theory of

 4. Relation Algebras And Their Application In Temporal And Spatial Reasoning The calculus of Relation algebras is an equational formalism; it tells us which Relations must exist, given several basic operations, such as Booleanhttp://portal.acm.org/citation.cfm?id=1057246

5. Representations For Small Relation Algebras
There are eighteen isomorphism types of finite Relation algebras with eight or fewer elements, and all of them are representable.
http://projecteuclid.org/handle/euclid.ndjfl/1040408612
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##### Representations for Small Relation Algebras
Source: Notre Dame J. Formal Logic Volume 35, Number 4 (1994), 550-562.
##### Abstract
There are eighteen isomorphism types of finite relation algebras with eight or fewer elements, and all of them are representable. We determine all the cardinalities of sets on which these algebras have representations. Primary Subjects: Full-text: Access granted (open access) Screen Optimized PDF File (121 KB) PDF File (97 KB) Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1040408612 Mathematical Reviews number (MathSciNet): Digital Object Identifier: doi:10.1305/ndjfl/1040408612 Zentralblatt Math identifier: back to Table of Contents
##### References
[1] Backer, F., Report for a seminar on relation algebras conducted by A. Tarski," Seminar Report , Berkeley, 1970.

6. In The Beginning There Were Algebras Of Concrete Relations
And he proved many interesting new results about Relation algebras, including a correspondence with 3variable logic that allowed the interpretation of set
http://www1.chapman.edu/~jipsen/talks/Tarski2001/Tarskitalk.htm
##### The many descendants of TarskiÂs Relation Algebras
Peter Jipsen Vanderbilt University
##### Alfred Tarski Centenary Conference, Warsaw, May 29, 2001
A story about the creation of Relation Algebras In the beginning there were algebras of concrete relations. Tarski saw they were good, and he separated the interesting ideas from the trivial ones. And Tarski said ÂLet there be an abstract theory about these algebrasÂ. So he made the theory of Relation Algebras. And he saw it was good. And then Tarski said ÂLet the theory produce all the known results about concrete relationsÂ. And it was so. And he proved many interesting new results about relation algebras, including a correspondence with 3-variable logic that allowed the interpretation of set theory and he provided the first example of an undecidable equational theory. And Tarski said ÂLet the minds teem with new conjectures, let ideas fly, and let the community produce many new related theories and resultsÂ. Thus the field of relation algebras was born, with its many applications and connections to other areas. (all quotes fictitious; passage based on well known source)

7. IngentaConnect Relation Algebras Of Intervals
Given a representation of a Relation algebra we construct Relation algebras of pairs and ofintervals . If the representation happens to be complete,
http://www.ingentaconnect.com/content/els/00043702/1996/00000083/00000002/art000
var tcdacmd="dt";

8. Atlas: Relation Algebras And Groups By Hajnal Andreka
A Relation algebra is any algebra (of the same similarity type as algebras of binary Relations) satisfying a certain finite set of equational
http://atlas-conferences.com/c/a/d/j/23.htm
 Atlas home Conferences Abstracts about Atlas Conference in Algebra (in honour of the 70th birthday of Ervin Fried) August 17-21, 1999 AlfrÃ©d RÃ©nyi Institute of Mathematics, Hungarian Academy of Sciences Budapest, Hungary Organizers LÃ¡szlÃ³ MÃ¡rki View Abstracts Conference Homepage Relation algebras and groups by Mathematical Institute, Budapest, Hungary Coauthors: Steven Givant (Mills Colege, Oaklanad, USA) An algebra of binary relations (or set relation algebra In the 1940s, Tarski put the theory on a modern footing. He introduced the concept of an abstract relation algebra and used algebraic and metamathematical techniques to study them. A relation algebra functional element is one that satisfies the equation x denotes the abstract operation of inversion, while ; denotes the abstract operation of relative composition and 1' denotes the identity element.) As a corollary they concluded that every relation algebra in which the Boolean unit is the sum of finitely many functional elements must also be representable. Finally, they proved that every atomic relation algebra in which the atoms are points is representable. (A point is an element that satisfies the equation x A diagonal element is one that is below the identity element 1'. A diagonal atom x is said to be

9. ARA - Automatic Relation Algebra Prover
ARA is an automatic theorem prover for various kinds of Relation algebras. It is based on Gordeev s Reduction Predicate Calculi for nvariable logic (RPC_n)
http://www-sr.informatik.uni-tuebingen.de/~sinz/ARA/
##### An Automatic Theorem Prover for Relation Algebras
ARA is an automatic theorem prover for various kinds of relation algebras. It is based on Gordeev's Reduction Predicate Calculi for n-variable logic (RPC_n) which allow first-order finite variable proofs. Using results from Tarski/Givant and Maddux we can prove validity in the theories of simple semi-associative relation algebras, relation algebras and representable relation algebras using the calculi RPC_3, RPC_4 and RPC_w. ARA is a Haskell-implementation that offers various reduction strategies for RPC_n, and a set of simplifications preserving n-variable provability.
The ARA prover is currently only available as a binary distribution for Solaris on the SPARC architecture and for Windows NT.
(gzip)
(zip)
##### Documentation
RA input language description (PS version) Besides this short input language description, there is no on-line documentation available so far. If you have any questions, feel free to contact the author (c) Carsten Sinz, January 2000

 10. JSTOR On Complete Atomic Proper Relation Algebras 1950 ON COMPLETE ATOMIC PROPER Relation algebras FRANK HARARY The object of this note is to classify the isomorphism types of all complete atomic properhttp://links.jstor.org/sici?sici=0022-4812(195009)15:3<197:OCAPRA>2.0.CO;2-L

11. Ian Hodkinson: Relational Bases Etc
Relational bases, Relation algebra cylindric algebra connections There are various connections between cylindric and Relation algebras,
http://www.doc.ic.ac.uk/~imh/frames_website/bases.html
##### Relational bases, relation algebra - cylindric algebra connections
Relation algebras are a common way to treat binary relations algebraically, and n-dimensional cylindric algebras handle n-ary relations. There are various connections between cylindric and relation algebras, and also between cylindric algebras of differing dimension. For example, taking the neat reduct This neat reduct process is closely related to first-order proof theory. Roughly, the laws holding in m-dimensional neat reducts of n-dimensional cylindric algebras correspond to the first-order sentences written with m variables (perhaps re-used) that can be proved using up to n variables. Finding an intrinsic characterisation of when an algebra is a reduct of another of larger dimension, and studying the hierarchy so induced, has been of interest to workers such as Maddux, Monk, and Tarski since the 1960s. Maddux developed the n-dimensional cylindric basis for this purpose, and the related notion of relational basis.

12. Relation Algebras With Preferences
Relation algebras are a wellestablished formalism for qualitative reasoning. In a Relation algebra, knowledge about Relations between entities such as
http://www.informatik.uni-freiburg.de/~ki/teaching/ss05/oberseminar/abstract-sci
##### Alexander Scivos
Relation algebras are a well-established formalism for qualitative reasoning. In a relation algebra, knowledge about relations between entities such as points, areas, or intervals is formally concluded, even under uncertainty of the relation. Then, unions of relations are used in which all relations have equal rank. However, this is not the way humans think. In case of uncertainty, we humans usually prefer some possible relations over others. In the talk, a formalization of this preference will be presented and formal criteria will be developed. With this formalization, the mental model preference can be applied in traditional reasoning algorithms, like Montari's path consistency algorithm. Moreover, it can be used as a heuristic for the backtracking procedure in CSPs over relation algebras that are known to be NPhard.

13. SFB/TR 8 - Project R3-[Q-Shape] - Research
Additionally they build up a Relation algebra with 24 basic Relations. The Conceptual Neighborhood Structure of the Dipole Relation algebras
http://www.sfbtr8.spatial-cognition.de/project/r3/QualitativeCalculi/DipoleCalcu
- Project R3-[Q-Shape]
##### Dipole Relation Algebra
In [ ] a qualitative spatial calculus dealing with two directed line segments, in the following also called dipole , as basic entities was presented. It is based on calculus presented by Schlieder in [ ]. These dipoles are used for representing spatial objects with intrinsic orientation. A dipole is defined by two points, the start point and the end point . The presented calculus deals with the orientation of two dipoles. An example of the relation is shown in the figure below . The four letters denote the relative position (e.g. left or right ) of one of the points to the other dipole:
The lrrr orientation relation between two dipoles
Based on a two dimensional continuous space, , the location and orientation of two different dipoles can be distinguished by representing the relative position of start and end points. In the original version by Schlieder no three points were allowed on a line resulting in 14 base relations [ ]. In [

14. [q-alg/9506004] On Deformations Of Commutation Relation Algebras
On Deformations of Commutation Relation algebras. Authors Robert Ra owski Comments 17 pages Reportno IFT UWr 890/95 Subj-class Quantum Algebra
http://arxiv.org/abs/q-alg/9506004
##### arXiv.orgq-alg
Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages
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##### Title: On Deformations of Commutation Relation Algebras
Authors: (Submitted on 6 Jun 1995) Abstract: This paper is on $C$ - symmetric creation and annihilation operators, which are constructed on Wick's algebras which fulfil consistency conditions. The essential assumption is that every algebraic action must be constant on equivalence classes. All consistency conditions follow from the above assumption. In this way we obtain well defined quotient algebras with some additional relations. Comments: 17 pages Subjects: Quantum Algebra (math.QA) Report number: IFT UWr 890/95 Cite as: arXiv:q-alg/9506004v1
##### Submission history
From: Ziemowit Popowicz [ view email
Tue, 6 Jun 1995 11:57:34 GMT (10kb)
Which authors of this paper are endorsers?
Link back to: arXiv form interface contact

15. The Algebra Of Logic: SchrÃ¶der
I of Principia Mathematica, and it has been a source of fundamental research under the name of Relation algebras in the school led by Tarski.
http://www.math.uwaterloo.ca/~snburris/htdocs/scav/schroeder/schroeder.html
 Previous: Frege Next: Peano Up: Supplementary Text Topics The monument to the work initiated by Boole, the algebraization of logic, is the three volumes Algebra der Logik Volumes I and II are devoted to the Calculus of Classes, with the standard operations of union, intersection and complement, adhering to Boole's arithmetic notation for union (+) and intersection ( ) the primitive notion, whose properties are given axiomatically (what we now call the axioms for a bounded lattice, presented as a partially ordered set), then defining the other operations and equality from it. getting a handle on the consequences of any premisses, or at least the fastest methods for obtaining these consequences, seems to me to be the noblest, if not the ultimate goal of mathematics and logic. from some hypotheses about classes it is often the case that some of the classes in the hypotheses do not appear in the conclusion. If one could find a such that then one could concentrate on the apparently simpler problem of deriving from . Finding

16. Relation Algebras Over Containers And Surfaces
Relation algebras over Containers and Surfaces An Ontological Study of a Room Space. Max Egenhofer and Andrea RodrÃ­guez Spatial Cognition and Computation 1
http://www.spatial.maine.edu/~max/RJ37.html
##### Relation Algebras over Containers and Surfaces: An Ontological Study of a Room Space
nedstatbasic("ACBShA0oWwPAaNNgL+FaeQnDb84g", 0); Max Egenhofer and
Spatial Cognition and Computation
##### Abstract

 17. Connections Between Quasi-projective Relation Algebras And Cylindric Algebras - InformaciÃ³n del artÃ­culo Connections between quasiprojective Relation algebras and cylindric algebras.http://dialnet.unirioja.es/servlet/articulo?codigo=2323779

18. DBLP: Ivo DÃ¼ntsch
3, Ivo DÃ¼ntsch Rough Relation algebras. Fundam. Inform. 21(4) 321331 (1994). 2, Ivo DÃ¼ntsch A Microcomputer Based System for Small Relation algebras.
http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/d/D=uuml=ntsch:Ivo.htm
 List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... Lech Polkowski : Transactions on Rough Sets VI, Commemorating the Life and Work of Zdzislaw Pawlak, Part I Springer 2007 EE Dimiter Vakarelov : Region-based theory of discrete spaces: A proximity approach. Ann. Math. Artif. Intell. 49 EE Beata Konikowska : A Multi-modal Logic for Disagreement and Exhaustiveness. Fundam. Inform. 75 EE Ewa Orlowska : Relational Attribute Systems II: Reasoning with Relations in Information Structures. T. Rough Sets 7 Wendy MacCaull Michael Winter Springer 2006 ... Michael Winter : Topological Representation of Contact Lattices. RelMiCS 2006 EE Alasdair Urquhart : Betweenness and Comparability Obtained from Binary Relations. RelMiCS 2006 EE Ewa Orlowska Anna Maria Radzikowska : Lattice-Based Relation Algebras II. Theory and Applications of Relational Structures as Knowledge Instruments 2006 EE Michael Winter : Rough Relation Algebras Revisited. Fundam. Inform. 74 Dominik Slezak Guoyin Wang Marcin S. Szczuka ... Yiyu Yao : Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, 10th International Conference, RSFDGrC 2005, Regina, Canada, August 31 - September 3, 2005, Proceedings, Part I Springer 2005 EE Ewa Orlowska Ingrid Rewitzky ... Michael Winter : Weak Contact Structures.

 19. RELATION ALGEBRAS OF ACTION AND INDETERMINACY We will refine the techniques in actual applications of branching time, multiintervals, algebras of action, probabilistic Relation algebras, planning withhttp://gow.epsrc.ac.uk/ViewGrant.aspx?GrantRef=GR/K54946/01

 20. Mathematical Structures Relation Algebras $\begin{array}{lr} http//localhost/gap/ramaddux.html Small Relation algebras f(1)= 1\\ f(2)= 1\\ f(3)= 0\\ f(4)= 3\\ f(5)= 0\\ f(6)= 0\\http://math.chapman.edu/cgi-bin/structures?Relation_algebras 21. UNIVERSAL ALGEBRA, ALGEBRAIC LOGIC AND DATABASES By BORIS PLOTKIN THE CATEGORIAL APPROACH TO ALGEBRAIC LOGIC Relation algebras Notes on quantifiers Definition of Relation algebras Another approach Relational algebras http://www.mmsysgrp.com/plotkin.htm ##### UNIVERSAL ALGEBRA, ALGEBRAIC LOGIC AND DATABASES by BORIS PLOTKIN (Kluwer Academic Press,1994) return to Mathematical Structures Group 22. Spir@l - Imperial College Digital Repository: Strongly Representable Atom Struct Title, Strongly representable atom structures of Relation algebras. Item Type, Journal. Author(s), Hirsch, R Hodkinson, I http://eprints.imperial.ac.uk/handle/10044/1/571  Advanced Search Imperial College Digital Repository Spir@l Home ... Submit Date Note: Your browser does not support javascript or you have javascript turned off. Although this will not affect your accessibility to the content of this site, some of the advanced navigation features may not be available to you. Home Title Author Issue Date ... Logic and Artificial Intelligence Please use this identifier to cite or link to this item: http://hdl.handle.net/10044/1/571 Files in This Item: File Content Version Size Format strorep.pdf Published (author's copy) Peer Reviewed 241.62 kB Adobe PDF View/Open Title: Strongly representable atom structures of relation algebras Item Type: Journal Author(s): Hirsch, R Hodkinson, I Content Version: Published (author's copy) Peer Reviewed Issue Date: Citation: P AM MATH SOC Vol.( 130 ) No.( 6 ) pp 1819 - 1831 URI: http://hdl.handle.net/10044/1/571 Publisher Link: http://dx.doi.org/10.1090/S0002-9939-01-06232-3 ISSN: First published in Proceedings of the American Mathematical Society in Volume 130 issue 6, 2002. Published by the American Mathematical Society Appears in Collections: Logic and Artificial Intelligence View License Imperial College London 23. Relation Algebras, 150 - Elsevier Relation algebras, 150. To order this title, and for more information, click here. This book belongs to the subject area Mathematics http://www.biolc.com/wps/find/bookreviewform.librarians/706796  Home Site map Elsevier websites Alerts ... Relation Algebras, 150 Book information Product description Audience Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view RELATION ALGEBRAS, 150 To order this title, and for more information, click here This book belongs to the subject area Mathematics Submit your review Your review is highly appreciated. You can use this form to share your opinion on this book with others. Please focus your comments on the content of the book. This review will be submitted to the publishing section of this book. All fields marked with * are compulsory Rating*: Poor Excellent Review (max. 5000 characters)*: From*: Your name: Keep me anonymous E-mail: Printer-friendly version Home Site map Terms and Conditions ... Feedback A Reed Elsevier company Elsevier B.V. 24. Relation Algebras From Cylindric And Polyadic Algebras -- Nemeti And Simon 5 (4) This paper is a survey of recent results concerning connections between Relation algebras (RA), cylindric algebras (CA) and polyadic equality algebras (PEA) http://jigpal.oxfordjournals.org/cgi/content/abstract/5/4/575 @import "/resource/css/hw.css"; @import "/resource/css/igpl.css"; Skip Navigation Oxford Journals Logic Journal of IGPL 1997 5(4):575-588; doi:10.1093/jigpal/5.4.575 Oxford University Press This Article Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive ... Request Permissions Google Scholar Articles by Nemeti, I Articles by Simon, A Search for Related Content ##### Relation algebras from cylindric and polyadic algebras I Nemeti and A Simon Mathematical Institute, Hungarian Academy of Sciences, Budapest PF. 127, H-1364 Hungary. Email: andras@math-inst.hu This paper is a survey of recent results concerning connections between relation algebras (RA), cylindric algebras (CA) and polyadic equality algebras (PEA). We describe exactly which subsets of the standard axioms for RA are needed for axiomatizing RA over the RA-reducts of CA 's, and we do the same for the 25. Preprints Of The Algebraic Logic Dept. Hajnal AndrÃ©ka Complexity of equations valid in algebras of Relations III IstvÃ¡n NÃ©meti and AndrÃ¡s Simon Relation algebras from cylindric and http://www.math-inst.hu/pub/algebraic-logic/Contents.html ##### Preprints of the Algebraic Logic Department Please note that this page (and the ftp site of the AL dept.) contains only a subset of the papers that are available electronically. If you know of a paper by a member of the dept., and would like to see it here, contact him/her. If you have problems retrieving a paper listed here, please let me know. 26. MATHS: Three Or More Infix Operators Maddux96 Relation algebras have a long history and can be used in a natural way .. However, there are an infinity of Relation algebras that are not http://www.csci.csusb.edu/dick/maths/math_45_Three_Operators.html Skip Navigation CSUSB CNS Comp Sci Dept ... Contact ] [Search Tue Sep 18 15:18:31 PDT 2007 ##### Contents ##### Three or More Infix operators The basis is • ALGEBRA Tarski turns up in most specialized systems. ##### High School Identities Burris & Lee 93, Stanley Burris and Simon Lee, "Tarski's High School Identities", American Math Monthly V100n3(Mar 93) pp231-236 • abstracted from the high school algebra of integers wthout powers. • ALGEBRA • ::infix(Set). • ::infix(Set). • STANDARD • ::Set. • For x,y,z:Set. • x+y=y+x. • x+(y+z)=(x+y)+z. • x*1=x. • x*y=y*x. • x*(y*z)=(x*y)*z. • x*(y+z)=(x*y)+(x*z). • HSI abstracted from the high school algebra of integers with powers. • basis (^) ::infix(A). • priority • 1^x = 1, • x^1 = x, • x^(y+z) = (x^y) * (x^z), • (x*y)^z = (x^z) * (y^z), • (x^y)^z = x^(y*z). [click here if you can fill this hole] HSI • above (Nat, +, *,^,1) in$
• above For many H: $HSI Suppose that NAT is the system of logic that describes the natuural numbers: Nat=$ NAT
• above
• Wilkie 80, "On exponentiation - a solution to Tarski's high school algebra problem", preprint, Oxford University, 1980.
• W (x,y)::=( ((1+x)^y+(1+x+x^2)^y)^x*((1+x^3)^x+(1+x^2+x^4)^x)^y) = ((1+x)^x +(1+x+x^2)^x)^y * ((1+x^3)^y + (1+x^2+x^4)^y)^x).
• 27. Tuesday, August 29
Finite symmetric integral Relation algebras with no 3cycles. 10.00, Wolfram Kahl. Semigroupoid interfaces for Relation-algebraic programming in Haskell
http://www.cs.man.ac.uk/relmics06/schedule.php
Conference Pictures Overview Schedule ... Sponsors Schedule Tuesday Wednesday Thursday Friday ... Saturday
##### Tuesday, August 29
Main entrance area Registration RelMiCS/AKA 2006 Main entrance area RelMiCS/AKA Welcome Reception Fossil Gallery, Manchester Museum
##### Wednesday, August 30
Registration Welcome Session 1 Chair: Renate Schmidt Invited talk: Roger Maddux Finite symmetric integral relation algebras with no 3-cycles Wolfram Kahl Semigroupoid interfaces for relation-algebraic programming in Haskell Coffee Session 2 Chair: Peter Jipsen Rudolf Berghammer Computing and visualizing lattices of subgroups using relation algebra and RelView Marcelo Frias, Rodolfo Gamarra, Gabriela Steren and Lorena Bourg Monotonicity analysis speeds up verification Britta Kehden Evaluating sets of search points using relational algebra Lunch Session 3 Chair: Ewa Orlowska Giuseppe Scollo, Giuditta Franco and Vincenzo Manca A relational view of recurrence and attractors in state transition dynamics Tadeusz Litak Algebraization of hybrid logic with binders Coffee Session 4 Chair: Marcelo Frias Michael Winter Weak relational products Gunther Schmidt Relational measures and integration Yasuo Kawahara On the cardinality of relations
##### Thursday, August 31

 28. OUP: UK General Catalogue This work presents a systematic study of decision problems for equational theories of algebras of binary Relations (Relation algebras).http://www.oup.com/uk/catalogue/?ci=9780821805954

29. Relation Algebras, Studies In Logic And The Foundations Of Mathematics - MADDUX,
Relation algebras, Studies in Logic and the Foundations of Mathematics; MADDUX, ROGER DUNCAN,. Offered by Black Oak Books, Berkeley.
http://www.antiqbook.com/boox/blac/588868.shtml
 ANTI Q BOOK Search Antiqbook Ask a question or Order this book Browse our books ... Book dealer info MADDUX, ROGER DUNCAN, Relation Algebras, Studies in Logic and the Foundations of Mathematics Elsevier, 2006. 8vo - over 7Â¾" - 9Â¾" tall, Hardcover, Cloth, Good. Vol. 150; price sticker on back cover; binding tight; interior, cover, and edges clean and intact. US$120.00 Offered by: Black Oak Books, Berkeley - Book number: 588868 See more books from our catalog: Mathematics Rare Books Hundreds of the world's finest antiquarian and used booksellers offer their books on Antiqbook. They offer full satisfaction and normal prices - no markups, no hidden costs, no overcharged shipping costs. 7 million books at your fingertips! Search all books at Antiqbook 30. Relation Algebras Date Tue, 28 Jan 92 120621 EST To linear@cs.stanford.edu The following note is from Jim Lambek The Relation algebra model proposed by Thomas Streicher http://www.cis.upenn.edu/~bcpierce/types/archives/1992/msg00023.html [Prev] [Next] [Index] [Thread] ##### Relation algebras Date: Tue, 28 Jan 92 12:06:21 EST To: linear@cs.stanford.edu The following note is from Jim Lambek: The relation algebra model proposed by Thomas Streicher for non-commutative linear logic has been studied in some detail by J. Lambek in "From categorial grammar to bilinear logic", which will appear in "Substructural logics", edited by K. Dozen and P. Schroeder-Heister, to be published by Oxford University Press. 31. Personal Homepage For R. D. Maddux Finite symmetric integral Relation algebras with no 3cycles . Experts on Relation algebras may be able to decipher the data in these files http://www.math.iastate.edu/maddux/ ##### R. D. Maddux Professor of Mathematics (and Professor of Computer Science and member of the faculties of E.E.B., C.A.S., and B.C.B.) Ph. D., University of California, Berkeley, 1978 Research Areas: logic, algebra, relation algebras Contact Information: Office: 418 Carver Hall, Iowa State University, Ames, IA 50011 515-294-8134 voice 515-294-5454 fax E-mail: maddux@iastate.edu Mailing Address: Department of Mathematics 396 Carver Hall Iowa State University Ames, Iowa 50011, USA LAST UPDATE: 31 July 2007 Office hours: none (sabbatical until August 2008) Current courses: none (sabbatical until August 2008) Curriculum Vitae from 2005: CV May 2005 (pdf) CV May 2005 (dvi) My Mathematical and Philsophical Genealogy: (txt) Slides for a talk at OAL2007 (a conference at Vanderbilt Univ., June, 2007): "Relevance logic and the calculus of relations" Slides for a talk at RelMiCS'06 (a conference at Manchester, UK, Sept 2006) "Finite symmetric integral relation algebras with no 3-cycles" Experts on relation algebras may be able to decipher the data in these files: 102survey.pdf  32. CAT.INIST Given a representation of a Relation algebra we construct Relation algebras of pairs and of intervals. If the representation happens to be complete,http://cat.inist.fr/?aModele=afficheN&cpsidt=3127397  33. Mathematics The modern theory of algebras of binary Relations, More reformulated by Tarski as an abstract, algebraic, equational theory of Relation algebras,http://shopping.msn.com/results/mathematics/bcatid162/forsale?text=category:math 34. Tarski 100 A brief history of Relation algebras, Victor Marek Tarski and semantical considerations in Logic Programming and Logical Foundations of Artificial http://www.mimuw.edu.pl/TARSKI/Tarski100.html ##### Programme of the Tarski Centenary Conference ##### Monday, 28 May ##### Morning session ##### Mathematical Institute, 8, Sniadeckich street, 4th floor, room 403 Opening John W. Addison Jr., Tarski's theory of definability: common themes in descriptive set theory, recursive function theory, classical pure logic, and finite-universe logic. break Solomon Feferman, Tarski's conception of logic ##### Afternoon sessions Mathematical Institute Banach Centre room 403A (Truth and semantics) room 403B (Foundations of mathematics) room 13 (Philosophical logic) room 14 (Algebra) Vladimir L. Vasyukov Developing Tarski: a Brouwerian Topos of Theories Angus Macintyre Quantifier elimination in geometrical situations, from real closed fields to rigid analytic spaces Janusz Czelakowski, Abstract algebraic logic and hierarchies of deductive systems Mai Gehrke Canonical extensions of bounded distributive lattice expansions Mario Gomez-Torrente Reading the "Wahrheitsbegriff" Ludomir Newelski Small profinite structures Don Pigozzi Abstract Algebraic Logic and the Specification of Abstract Data Types break break break break Arianna Betti Lesniewski's Early Solution to the Liar and Tarski Lev Beklemishev Provability algebras and proof-theoretic ordinals Leo Esakia Recent observations concerning Tarski's topological interpretation of the Intuitionistic Calculus Matt Valeriote Decidable Equationally Defined Classes 18:00 Reception by the Rector of Warsaw University ( at Palac Kazimierzowski ##### Alfred Tarski memory session ##### 19:30, Warsaw University, 26/28 Krakowskie Przedmiescie street, Palac Kazimierzowski, Senate Hall 35. Citations: Varieties Of Relation Algebras - Jonsson (ResearchIndex) B. Jonsson. Varieties of Relation algebras. Algebra Universalis, 15273298, 1982. http://citeseer.comp.nus.edu.sg/context/549955/0  7 citations found. Retrieving documents... J'onsson, B., Varieties of Relation Algebras , Algebra Universalis 15, 1982, pp273 298. @ NUS Home/Search Document Not in Database Summary Related Articles Check This paper is cited in the following contexts: Pair-Dense Relation Algebras - Maddux (1991) (5 citations) (Correct) ....that section. To get the second theorem we use Monk s results in [Mo70] on the existence of completions of relation algebras. In x7 we define points, pairs, twins, functional elements, and identity atoms, and prove many things about them. That section contains generalizations of some theorems in and [SS85] There is only one theorem in that section which holds for relation algebras but not for semiassociative relation algebras. This is exactly where to look to see why the algebra in (A) must be a relation algebra. In x8 we study point density and pair density. Highlights from this .... ....necessary for later results in this paper. For each of these three classes this section contains theorems collecting various identities and implications for arbitrary elements and for atoms. The most extensive source of arithmetical results for relation algebras is [CT51] Other good sources are , JT52] and [Ma82] The notions of complete additivity and normality for operators on Boolean algebras are defined in [JT51] Definition 1.  36. Baztech Informacja O Publikacji Tytul Relations algebras in qualitative spatial reasoning In this paper we investigate Relation algebras obtained from dixfferent notions ofhttp://baztech.icm.edu.pl/baztech/cgi-bin/btgetdoc.cgi?BUS1-0007-0060 37. A Pseudo Representation Theorem For Various Categories Of Relations Furthermore, we use our concept of a basis to extend a known result from the theory of heterogeneous Relation algebras. Keywords Relation Algebra, Dedekind http://www.tac.mta.ca/tac/volumes/7/n2/7-02abs.html ##### A Pseudo Representation Theorem for Various Categories of Relations ##### M. Winter Keywords: Relation Algebra, Dedekind category, Allegory, Representability, Matrix Algebra. 2000 MSC: 18D10,18D15,03G15. Theory and Applications of Categories , Vol. 7, 2000, No. 2, pp 23-37. http://www.tac.mta.ca/tac/volumes/7/n2/n2.dvi http://www.tac.mta.ca/tac/volumes/7/n2/n2.ps http://www.tac.mta.ca/tac/volumes/7/n2/n2.pdf ftp://ftp.tac.mta.ca/pub/tac/html/volumes/7/n2/n2.dvi ... TAC Home 38. Relation Algebras By Games - Libro - Robin Hirsch, Ian Hodkinson - Editore North Relation algebras by Games, Robin Hirsch, Ian Hodkinson. This is the first modern book on Relation algebra and contains original research which is not http://www.libreriauniversitaria.it/relation-algebras-by-games-robin/book/978044 PowerSearch: Libri Italiani Libri Inglesi Libri Tedeschi DVD Videogames Tutti i reparti ##### Relation Algebras by Games ##### di Robin Hirsch Ian Hodkinson • Prezzo: Questo libro ha diritto alla spedizione gratuita Leggi i dettagli DisponibilitÃ : Normalmente disponibile in 15/20 giorni lavorativi Metti nel carrello (Puoi sempre toglierlo dopo) ##### Descrizione This is the first modern book on relation algebra and contains original research which is not available elsewhere. Following an intuitive games-based approach, the book uses combinatorial games to develop some of the theory of relation algebras, focusing on the fundamental notion of representation. ##### Dettagli del libro ##### Recensioni degli utenti Scrivi una nuova recensione e condividi la tua opinione con altri utenti. ##### Segnala a un amico Segnala Relation Algebras by Games ad un amico.  39. Seminars @ CECS The set of all binary Relations on a nonempty set is called the algebra of The subclass of Relation algebras that are isomorphic to a subalgebra of thehttp://cecs.anu.edu.au/seminars/showone.pl?SID=417  40. Function Algebras On Finite Sets - Mathematical Logic And Foundations Journals, The second part on fuction algebras covers the following topics Galoisconnection between function algebras and Relation algebras, completeness criterions,http://www.springer.com/west/home/math?SGWID=4-10042-22-173667303-0  41. [Abstract] Demonic Semantics Of Guarded Commands Monotype/residual Style 2 Relation Algebra 2.1 Definition and basic laws Both homogeneous and In this paper, we use heterogeneous Relation algebras whose defini tion is takenhttp://actapress.com/PDFViewer.aspx?paperId=13296  42. Sibirskii Matematicheskii Zhurnal On quasiidentities of Relation algebras with Diophantine operations D. A. Bredikhin UDC 519.4 Received 04.09.1995http://www.mathnet.ru/php/journal.phtml?wshow=paper&jrnid=smj&paperid=419&year=1  43. Relation Algebras By Games Is Available From Bestprices.com Books! Relation algebras by Games only$185.06, get the Relation algebras by Games book From BestPrices.com!http://www.bestprices.com/cgi-bin/vlink/0444509321?id=nsession

44. Scientific Commons Rough Relation Algebras (1993), 1993-12-09
Rough Relation algebras were introduced by S. Comer as a generalisation of algebras of Pawlak s rough sets and Tarski s Relation algebras.
http://en.scientificcommons.org/384198
 <Â·vÂÂ%wÂ1vJÃºÂsÂCÃEÂÂÂªÃ³k9ÂJLhÂ)

 45. Tower.com: Roger Duncan Maddux Relation Algebras Hardcover Tower.com Relation algebras Books Roger Duncan Maddux by Roger Duncan Maddux.http://www.tower.com/details/details.cfm?wapi=100266894

 46. Bentham Press - Engineering Books & Publications, Software And Training Relation algebras are algebras arising from the study of binary Relations. Part 4 presents some constructions of Relation algebras, including Monkhttp://www.bentham.com/publications/?id=1681&PHPSESSID=ca18d5b627b3b426725fde928

47. CiteULike: Tag Relation-algebras [1 Article]
Relations and Kleene Algebra in Computer Science (2006), pp. 235250. by Wolfram Kahl. posted to Relation-algebras haskell category-theory by mstone on
http://www.citeulike.org/tag/relation-algebras
##### Tag relation-algebras [1 article]
Recent papers classified by the tag relation-algebras.
• Semigroupoid Interfaces for Relation-Algebraic Programming in Haskell Relations and Kleene Algebra in Computer Science (2006), pp. 235-250. by Wolfram Kahl posted to relation-algebras haskell category-theory by mstone on 2007-08-21 06:25:28 as
RIS
##### Related Tags
Tags related to: relation-algebras Filter: category-theory haskell CiteULike organises scholarly (or academic) papers or literature and provides bibliographic (which means it makes bibliographies) for universities and higher education establishments. It helps undergraduates and postgraduates. People studying for PhDs or in postdoctoral (postdoc) positions. The service is similar in scope to EndNote or RefWorks or any other reference manager like BibTeX, but it is a social bookmarking service for scientists and humanities researchers.

48. Front: [q-alg/9506004] On Deformations Of Commutation Relation Algebras
Title On Deformations of Commutation Relation algebras Authors Robert Ra owski Categories math.QA Quantum Algebra Comments 17 pages
http://front.math.ucdavis.edu/9506.5144
 Front for the arXiv Mon, 24 Dec 2007 Front math QA q-alg/9506004 search register submit journals ... iFAQ q-alg/9506004 Title: On Deformations of Commutation Relation Algebras Authors: Robert RaÃÂowski Categories: math.QA Quantum Algebra Comments: 17 pages Report number: IFT UWr 890/95 Abstract: This paper is on $C$ - symmetric creation and annihilation operators, which are constructed on Wick's algebras which fulfil consistency conditions. The essential assumption is that every algebraic action must be constant on equivalence classes. All consistency conditions follow from the above assumption. In this way we obtain well defined quotient algebras with some additional relations. Owner: Ziemowit Popowicz Version 1: Tue, 6 Jun 1995 11:57:34 GMT - for questions or comments about the Front arXiv contact page - for questions about downloading and submitting e-prints

49. Relation Algebra - Wikipedia, The Free Encyclopedia
In mathematics, a Relation algebra is a residuated Boolean algebra supporting an involutary unary operation called converse. The motivating example of a
http://en.wikipedia.org/wiki/Relation_algebra
var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
##### Relation algebra
Relation algebra is different from relational algebra , a framework developed by Edgar Codd in 1970 for relational databases
In mathematics , a relation algebra is a residuated Boolean algebra supporting an involutary unary operation called converse. The motivating example of a relation algebra is the algebra 2 X of all binary relations on a set X , with R S interpreted as the usual composition of binary relations . Early forms of relation algebra emerged in the 19th century with the work of Augustus De Morgan Charles Peirce , and Ernst SchrÂ¶der . Its present-day purely equational form was developed by Alfred Tarski and his students starting in the 1940s.
##### edit Definition
A relation algebra L I ) is an algebraic structure such that
(i) ( L I , Ã¢ÂÂ·, Ã¢ÂÂ) is a residuated Boolean algebra , and (ii) the unary operation x satisfies x I x I x
Since x y can be defined in terms of composition and converse as x y , and dually x y as x y , it is not necessary to include Ã¢ÂÂ· or Ã¢ÂÂ in the signature, which can therefore be simplified to ( L I ), the more usual form of the signature for relation algebras. On the other hand

50. A Ternary Relation Algebra Of Directed Lines
We define a ternary Relation Algebra (RA) of relative position Relations on twodimensional directed lines (d-lines for short). A d-line has two degrees of
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A ternary Relation Algebra of directed lines Authors:
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Computer Science - Artificial Intelligence, I.2 (I.2.4) Comment:
60 pages. Submitted. Technical report mentioned in "Report-no" below is an earlier version of the work, and its title differs slightly (Reasoning about relative position of directed lines as a ternary Relation Algebra (RA): presentation of the RA and of its use in the concrete domain of an ALC(D)-like description logic) Bibliographic Code:
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51. Interacting State Machines: A Stateful Approach To Proving Security
Abstract We present a theorem proving system for abstract Relation algebra called RALL (= RelationAlgebraic Language and Logic), based on the generic
http://david.von-oheimb.de/cs/papers/RALL.html
##### Publication
RALL: Machine-supported Proofs for Relation Algebra
Conference on Automated Deduction CADE-14 Author: David von Oheimb , Thomas F. Gritzner
Year:
Publisher:
Springer LNCS 1249
Editor: William McCune
Abstract: We present a theorem proving system for abstract relation algebra called RALL (= Relation-Algebraic Language and Logic), based on the generic theorem prover Isabelle. On the one hand, the system is an advanced case study for Isabelle/HOL,and on the other hand, a quite mature proof assistant for research on the relational calculus.RALL is able to deal with the full language of heterogeneous relation algebra including higher-order operators and domain constructions, and checks the type-correctness of all formulas involved. It offers both an interactive proof facility, with special support for substitutions and estimations, and an experimental automatic prover. The automatic proof method exploits an isomorphism between relation-algebraic and predicate-logical formulas, relying on the classical universal-algebraic concepts of atom structures and complex algebras.
Pre-print version available as compressed Postscript and PDF file.

52. Algebra Of Programming Research Group: 1996 Minutes
As such, sequential algebra is a natural candidate for modelling (imperative) programs. In fact, it is only a slight generalization of Relation algebra in
http://web.comlab.ox.ac.uk/oucl/research/pdt/ap/minutes/minutes1996.html
##### Minutes of Meetings of the Algebra of Programming Research Group in 1996
The schedule for Hilary Term 1996 was as follows:
Week 5: 16 Feb, Richard Miller , University of Oxford
Multi-dimensional arrays and the empty array.
Week 6: 23 Feb, Grant Malcolm , University of Oxford
How can programs be made less efficient?
Week 7: 1 March, Quentin Miller , University of Oxford
Graph Manipulation on BSP Computers.
Week 8: 8 March, Paul Rudin , University of Oxford
Graphical Calculus Completness.
The schedule for Michaelmas Term 1996 was as follows:
Week 0: Oct 11, Ian Hayes , University of Queensland
Coercing Real-Time Refinement.
Week 1: Oct 18, Wim Feijen , Technical University of Eindhoven
The Derivation of Multi-Programs. (Lecture theatre).
Week 2: Oct 25, Richard McPhee , University of Oxford
Compositional Logic Programming.
Week 3: Nov 1, Bernard Sufrin , University of Oxford
Unification and Jape.
Week 4: Nov 8, Burghard von Karger , University of Kiel
Temporal and Sequential Algebra.
Week 5: Nov 15, Jifeng He , University of Oxford
Week 6: Nov 22

53. Relational Algebra
Operators in Relational algebra are not necessarily the same as SQL operators DELETE provides a condition on the attributes of a Relation to determine
http://db.grussell.org/section010.html
Next Page Up One Level Lecture Slides available: PDF PowerPoint
##### Contents
In order to implement a DBMS, there must exist a set of rules which state how the database system will behave. For instance, somewhere in the DBMS must be a set of statements which indicate than when someone inserts data into a row of a relation, it has the effect which the user expects. One way to specify this is to use words to write an `essay' as to how the DBMS will operate, but words tend to be imprecise and open to interpretation. Instead, relational databases are more usually defined using Relational Algebra. Relational Algebra is :
• the formal description of how a relational database operates an interface to the data stored in the database itself the mathematics which underpin SQL operations
Operators in relational algebra are not necessarily the same as SQL operators, even if they have the same name. For example, the SELECT statement exists in SQL, and also exists in relational algebra. These two uses of SELECT are not the same. The DBMS must take whatever SQL statements the user types in and translate them into relational algebra operations before applying them to the database.
##### Terminology
• Relation - a set of tuples.

54. CP1500 Tutorial Solution - Fun With Relational Algebra
More Formulating Queries in the Relational Algebra. Relational schemas for five relations in a movie database are depicted below.
http://www.it.jcu.edu.au/Subjects/cp1500/resources/docs/introToRA.soln.html
##### Relational Algebra Cheatsheet
Create a relational algebra cheatsheet. The cheatsheet should include each of the following operations: selection, projection, Cartesian product, union, intersection, difference, theta-join, equi-join, and natural join. For each operation you should
• list the operator symbol,
• give a three or four word intuitive, English description,
• whether the operation is unary or binary (takes one or two relations as arguments),
• give an example of how the operation is used,
• state the relationship (if any) of the degree of the result to the degree of the operands,
• state the relationship (if any) of the cardinality of the result to the cardinality of the operands,
• and state any restrictions on the use of the operator.
For the example of the use of the operation, use one or more of the following relations. student(id, name, address) JCUsubjects(code, lecturer) TAFEsubjects(code, lecturer) enrolledIn(id, code) You may break the cheatsheet into two (or more) tables if the rows get too big. Here is an example to get you started. A Relational Algebra cheatsheet - Part 1 English operation arity description selection R T unary union R S T binary create set of tuples from relations R and S A Relational Algebra cheatsheet - Part 2 English example restrictions selection code OR code JCUsubjects none union JCUsubjects TAFEsubjects R and S must be union-compatible A Relational Algebra cheatsheet - Part 3 English degree cardinality selection degree( R

55. NutshellMath Pre-Algebra - Relations And Functions
NutshellMath offers targeted math homework help including prealgebra tutorials on understanding and representing algebraic relations.
http://home.nutshellmath.com/en-US/nutshell_pages/html/demos_content/prealg_rela
 Textbooks Demos Glossary Terms Sign-up Today! ... Pre-Algebra > Relations and Functions Speed: Broadband Dialup/56k This pre-algebra math tutorial from NutshellMath offers targeted math homework help on understanding and representing relations. The instruction in this tutorial is focused on problems 2, 3, 8, 9, and 31-43 on pages 36 and 37 in the Pre-Algebra text from Glencoe Mathematics. Relations in algebra are stated associations of two variables represented by a collection of associated values. Such relations can be expressed as collection of ordered pairs, plotted points on a coordinate system, or a series of values in a table. Relations for the basis for nearly all of algebra, and are related to functions, which are general rules which describe relations. This tutorial focuses upon working with relations, and solving homework problems that involve representing algebraic relations as collections of ordered pairs, graphs or tables. To represent a relation as a set of ordered pairs, it is only necessary to write each set of associated values in parentheses and separated by a comma. Each ordered pair should be written with the x-value first, and then the y-value. To express a relation as a plot of points on a coordinate plane, first draw a coordinate plane, and plot each set of associated values at the corresponding point on the plane, x number of steps horizontally from the origin, and y steps vertically. To construct a table, list each set of associated values side-by-side in a two-column table, under the appropriate column heading; either x or y. Each of these methods is an acceptable way of representing a relation in algebra.

 56. Scheme Evolution And The Relationship Algebra. Revision, This paper discusses extensions to the conventional relational algebra to support both aspects of transaction time, evolution of a database s contents andhttp://stinet.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA

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