61. PSSL 98 logic 15.20 Rolf Rother (Bremen) Strengthening of homogeneity in categorical algebra 16.20 Libor Polák (Brno) On equational logic (for semigroups) 17.00 http://www.wraith.u-net.com/PSSL/1998.html

THE PERIPATETIC SEMINAR ON SHEAVES AND LOGIC Sixty-sixth Meeting: Birmingham, 2829 March 1998 Friday Paul Taylor (QMW) Two intertwined stories about induction and recursion Saturday Peter Johnstone (Cambridge) On (not-quite-)toposes of (not-quite-)coalgebras Enrico Vitale (Louvain) Picard and Brauer bigroups Adam Eppendahl (QMW) Arithmetic universes and pull-back theories Ralph Loader (Edinburgh) Yet more adequacy proofs Steve Vickers (Imperial) Sheaves and frame presentations Paola Maneggia (Birmingham) Polymorphism and logical predicates Paul Taylor (QMW) Quadrality Sunday Barney Hilken (Manchester) Sheaf models of modal logic Natasha Alechina (Birmingham) Relating Kripke and categorical semantics for intuitionistic modal logic Eike Ritter (Birmingham) On the semantics of classical disjunction Martin Hyland (Cambridge) Invariants and proofs Sixty-seventh Meeting: Utrecht, 3031 May 1998 Saturday John Power (Edinburgh) Higher-dimensional categories, I Ronnie Brown (Bangor) Computation of free crossed resolutions of groups Kirill Mackenzie (Sheffield) Duality for double structures Thomas Streicher (Darmstadt) A model for computable analysis George Janelidze (Tbilisi) Categorical, homological and universal-algebraic approach to central extensions

62. Category Theory (M24) tool for anyone doing research in topology, abstract algebra, mathematical logic or theoretical F. Borceux Handbook of categorical algebra, Cambridge UP, 1994. http://www.maths.cam.ac.uk/CASM/courses/descriptions/node30.html

Next: Combinatorial Set Theory (L24) Up: Logic Previous: Logic Category Theory (M24) P.T. Johnstone Category theory begins with the observation (Eilenberg-Mac Lane 1942) that the collection of all mathematical structures of a given type, together with all the maps between them, is itself an instance of a nontrivial structure which can be studied in its own right. In keeping with this idea, the real objects of study are not so much categories themselves as the maps between themfunctors, natural transformations and (perhaps most important of all) adjunctions. Category theory has had great success in the unification of ideas from different areas of mathematics; it has now become an indispensable tool for anyone doing research in topology, abstract algebra, mathematical logic or theoretical computer science (to name but a few). This course aims to give a general introduction to the basic grammar of category theory, without any (intentional!) bias in the direction of any particular application. It should therefore be of interest to a large proportion of pure Part III students. Categories, functors and natural transformations

63. Category Theory (M24) 2. Francis Borceux, Handbook of categorical algebra , Cambridge University Press (1994). next up previous Next Set Theory (M24) Up logic Previous logic Part http://www.maths.cam.ac.uk/CASM/courses/02-03/descriptions/node26.html

Next: Set Theory (M24) Up: Logic Previous: Logic Category Theory (M24) E. Cheng Category theory begins with the observation (Eilenberg-MacLane 1942) that the collection of all mathematical structures of a given type, together with all the maps between them , is itself an instance of a nontrivial structure which can be studied in its own right. In keeping with this idea, the real objects of study are not so much categories themselves as the maps between themfunctors, natural transformations and (perhaps most important of all) adjunctions. Category theory has had great success in the unification of ideas from different areas of mathematics; it has now become an indispensable tool for anyone doing research in topology, abstract algebra, mathematical logic or theoretical computer science (to name but a few examples). This course aims to give a general introduction to category theory, without any (intentional!) bias in the direction of any particular application. It should therefore be of interest to a large proportion of pure Part III students. Categories, functors and natural transformations.

64. Handbook Of Categorical Algebra: Volume 1, Basic Category Theory History of Calculus. History of logic. Mathematicians. Philosophy of Mathematics. Les Clewlow. Handbook of categorical algebra Volume 1, Basic Category Theory. http://mathematicsbooks.org/0521441781.html

Home Search High Volume Orders Links ... Philosophy of Mathematics Additional Subjects Fashion Illustration Now William Sleator Generals in Blue Lives of the Union Commanders: Lives of the Union Commanders Snakes of Georgia South Carolina ... The Call Goes Out: Interspecies Communication Handbook of Categorical Algebra: Volume 1, Basic Category Theory Written by Francis Borceux Published by Cambridge University Press (August 1994) ISBN 0521441781 Price $110.00 Look for related books on other categories Category Theory Mathematics Algebra - Linear Categories (Mathematics) Still didn't find what you want? Try Amazon search Search: All Products Books Magazines Popular Music Classical Music Video DVD Baby Electronics Software Outdoor Living Wireless Phones Keywords: Or try to look for Handbook of Categorical Algebra: Volume 1, Basic Category Theory at Fetch Used Books, at or at CampusI See Also Listen to Me Good: The Life Story of an Alabama Midwife Juan Felipe Herrera Tanganjika- Buntbarsche. Concrete Jungle Our Bookstores Cooking Books Games Books Computer Books Health Books ... Music Books Web Resources Amazon Australian Mathematics Trust European Mathematical Society (EMS) Kappa Mu Epsilon - Official Site ... Exchange links with us

65. IntroductionEssay the study of truth values and categorical the study of appears to be only one important algebraic structure that is common to topology, logic and (more http://mcs.open.ac.uk/cft36/IntroductionEssay.htm

From Topology, Logic and Category to the Geometric Mathematical Framework: Research Explained This page is intended as an essay for the educated but mathematically less sophisticated reader. From Logic to Algebra to Topology to Logic The study of logic in its own right has a long and distinguished history, and has experienced remarkable moments of clarity over the years; for example the introduction of the Boolean algebra whereby a deep connection was made between reasoning about truth in the abstract and a concrete algebraic structure. The study of algebra (as done by any school student) provides well established mathematical tools - the introduction of the Boolean algebra allowed these algebraic tools to be applied to the study of logic. The study of topology also has an illustrious history: on a basic level it is mankind's attempt to model the physical world in which we all move. One moment of clarity in topology was the introduction of the, now standard, definition of a topological space by Hausdorff early in the 20 th Century. This absolutely simple definition gave workers the ability to reason about all spaces and with few exceptions all discussion in mathematics about models of physical space use models that are examples of this definition. So, the spaces that are investigated by physicists today (or, developed by Einstein) are all examples of topological spaces.

66. ECS EPrints Service - On Specification Logics For Algebra-coalgebra Structures: 4. F. Borceux. Handbook of categorical algebra, volume 2. CUP, 1994. 7. B. Jacobs. Manysorted coalgebraic modal logic A model-theoretic study. Theoretical. http://eprints.ecs.soton.ac.uk/archive/00009116/

university A-Z sotONLINE home Research ... Members Area On specification logics for algebra-coalgebra structures: reconciling reachability and observability Cirstea, C. On specification logics for algebra-coalgebra structures: reconciling reachability and observability . In Proceedings of Foundations of Software Science and Computation Structures Conference , pages Grenoble, France Nielsen, M. and Engberg, U. , Eds. Downloads File type File size PDF - Requires Adobe Acrobat Reader or other PDF viewer. Abstract The paper builds on recent results regarding the expressiveness of modal logics for coalgebras in order to introduce a specification framework for coalgebraic structures which offers support for modular specification. An equational specification framework for algebraic structures is obtained in a similar way. The two frameworks are then integrated in order to account for structures comprising both a coalgebraic (observational) component and an algebraic (computational) component. The integration results in logics whose sentences are either coalgebraic (modal) or algebraic (equational) in nature, but whose associated notions of satisfaction take into account both the coalgebraic and the algebraic features of the structures being specified. Each of the logics thus obtained also supports modular specification. EPrint Type Conference or Workshop Item Keywords algebraic specification, equational logic, coalgebraic specification, modal logic

67. Homepage For Prof. Erwin Engeler Categories in model theory Models with prescribed secondorder properties. J. Symbolic logic 37 (1962) 476. categorical algebra, eds S. Eilenberg et al. http://www.math.ethz.ch/~darms/WWW/engeler/engeler-cv.html

Prof. Erwin Engeler Curriculum Vitae: Dates and Stations Activities and Offices Publications Classical model theory and infinitary languages ... Miscellaneous My address: Department of Mathematics Federal Institute of Technology 8092 Zurich, Switzerland Phone: + 41 1 632 22 25 How to contact me be email: engeler@math.ethz.ch Click here to visit the home page of my wife Dr. phil. Margaret Engeler. Dates and Stations Born in Schaffhausen, Switzerland on the 13th February 1930. Diploma in mathematics at the ETH, Zurich Dr.sc.math. ETH, Zurich (Prof. P. Bernays) Assistant Professor at the University of Minnesota Assistant Professor at the University of California, Berkeley Associate Professor and Full Professor at the University of Minnesota Professor of Logic and Computer Science, Mathematics Department, ETH, Zurich Activities and Offices Author of various books on Logic, Mathematics and Computer Science, translated into Russian, Japanese and Chinese Editor of scientific journals, book series and symposia Collected works 1993 Active interest in music, art and various outdoor sports

68. Mia Pagina Web My research interests include modal logics, categorical and algebraic logic, natural language semantics and automated reasoning. http://homes.dsi.unimi.it/~ghilardi/

SILVIO GHILARDI via Comelico 39 - 20135 Milano - Italy tel. +39/0250316217 - e-mail: ghilardi@dsi.unimi.it I was born in May 1958 near Bergamo. I have been living in Milano since I got married with Miriam Franchella in September 1993; I have three children (Lavinia, Virgilio and Tiberio). Here you can see a picture of me drawn by some students of mine. After a degree in Philosophy, I got a PhD in Mathematics in Milano. I was research assistant in Algebra and Geometry at the Mathematics Department of the University of Milano and then associate professor in Mathematical Logic at the Computer Science Department of the same University, where since march 2002, I am full professor in Logic and Philosophy of Science. My research interests include: modal logics, categorical and algebraic logic, natural language semantics and automated reasoning. Recent Publications (1999-2004): T. Brauner, S. Ghilardi First Order Modal Logic, in P. Blackburn, J. van Benthem, F. Wolter (eds.), Handbook of Modal Logic, Elsevier (in preparation). F. Baader, S. Ghilardi, C. Tinelli

69. From Owner-sbc-l@rio.cos.ufrj.br Thu Dec 5 072356 1996 Return within the framework of categorical logic, which will the the interpretation of intuitionistic logic in sheaves over a complete Heyting algebra, with examples http://www.di.ufpe.br/~ruy/categorical/concurrency

From owner-sbc-l@rio.cos.ufrj.br Thu Dec 5 07:23:56 1996 Return-Path: Received: from cos.ufrj.br (rio.cos.ufrj.br) by di.ufpe.br (4.1/SMI-4.1) id AA04527; Thu, 5 Dec 96 07:23:45 EST Received: by cos.ufrj.br (4.1/SMI-4.1) id AA13262; Thu, 5 Dec 96 08:22:20 EDT Received: from di.ufpe.br by cos.ufrj.br (4.1/SMI-4.1) id AA13256; Thu, 5 Dec 96 08:22:15 EDT Received: from pesqueira (pesqueira.di.ufpe.br) by di.ufpe.br (4.1/SMI-4.1) id AA04486; Thu, 5 Dec 96 07:19:44 EST Received: by pesqueira (5.x/SMI-SVR4) id AA20658; Thu, 5 Dec 1996 07:19:43 -0300 Date: Thu, 5 Dec 1996 07:19:43 -0300 From: XXXXX Message-Id: < FOR FURTHER INFORMATION CONTACT: Ruy Guerra de Queiroz Departamento de Informatica Universidade Federal de Pernambuco (UFPE) Caixa Postal 7851 50732-970 Recife, PE Brazil E-mail: XXXXX tel: +55 81 271 8430 fax: +55 81 271 8438

70. CoMeta - Computational Metamodels - Home approaches to concurrency and mobility (such as Tile Logics, double categories, graph transformation systems, bialgebras, and the categorical algebra of cospan http://cometa.dimi.uniud.it/

CoMeta - Computational Metamodels Home Meetings Documents and Reports Publications ... Tools NEWS The final workshop of the project is approaching! Description The CoMeta project is partially funded by the Ministero dell'Istruzione, Università e Ricerca (MIUR) . The project number is COFIN 2001013518. The duration is 24 months (2002-2003). Scientific Coordinator: Furio Honsell Principal Partners and Contacts: Dipartimento di Scienze Chimiche, Fisiche e Matematiche, Università dell'Insubria - Nicoletta Sabadini Dipartimento di Informatica, Università di Pisa - Ugo Montanari Dipartimento di Informatica, Università di Torino - Mariangiola Dezani Dipartimento di Matematica e Informatica, Università di Udine - Marino Miculan Summary of Project Computer Science has grown into a complex discipline, with scientific and technological sides to it, which intersects various knowledge domains at once, and acts at various levels of abstraction. In order to put into focus the present project, it appears convenient to distinguish two metalevels, above the basic one, which is the one where hardware and software systems live. The semantical and syntactical tools which are normally used to specify and analyze the object level systems appear on the first of these metalevels. This is the abstraction level of programming and specification languages, of calculi, of denotational and operational models, of automata, of Petri Nets, etc., but it is also the level of the logical systems used in verfying and analyzing properties of programs and processes, etc.

71. Fields Of Research Work Hyperequational Theory and Hyperequational logic. Algebraic properties of monoids of hypersubstitutions categorical Equivalences of Quasivarieties and of Clones. http://users.math.uni-potsdam.de/~denecke/forschun.htm

Fields of research work General Algebra, Category Theory and Applications in Discrete Mathematics, Theoretical Computer Science and Mathematical Logic Objects of the algebraic research work of the group "General Algebra and Discrete Mathematics" are algebraic structures which are relevant for Discrete Mathematics, Theoretical Computer Science and Logic. The research methods are based on General Algebra and Category Theory and typical methods of these areas are used. The results should be applicable in other theoretical fields like Theoretical Computer Science, Mathematical Logic, Graph Theory and Combinatorics and should have influence to the development of General Algebra. The generality of our approach allows to study all kinds of algebraic structures, even such ones which become of recent actual interest. We want to generalise particular algebraic results and want to classify algebraic structures under new viewpoints. Therefore, in the following years partial algebras, classes of partial algebras and multibased algebras will become important in our research work. Further, the results on classes of algebraic structures and their logical description will be applied in the Theory of Automata and in the Theory of Formal Languages.

72. Comp.compilers: Final CfP: AMAST'93 build programs from such specifications, extraction of programs from constructive proofs, categorical, algebraic and logic programming, deductive databases http://compilers.iecc.com/comparch/article/92-12-013

Final CfP: AMAST'93 From comp.compilers Newsgroups: comp.compilers From: scollo@cs.utwente.nl (Pippo Scollo) Organization: University of Twente, Dept. of Computer Science Date: Fri, 4 Dec 1992 20:31:13 GMT Keywords: CFP - special interest on mathematical education of software developers - one-day extension of the conference dates - extension of submission deadline to 8 January 1993 (sharp!) FINAL CALL FOR PAPERS Third International Conference on Algebraic Methodology and Software Technology, AMAST University of Twente, The Netherlands June 21-25, 1993 Goals and Organization The goal of the third AMAST conference to be held on June 21-25, 1993, at the University of Twente, Enschede, The Netherlands, is to consolidate the trend towards using algebraic methodology as a foundation for software technology, and to show that universal algebra provides a practical mathematical alternative to the common, ad-hoc approaches to software

73. A Report On LACS A Tribute To Helena Rasiowa valued logic, philosophical roots of logic, lambda calculus, proof theory, finite model theory, algebraic and categorical methods in logic, reasoning about http://www.iarcs.org.in/activities/newsletter/vol2-1/rasiowa.html

A Report on LACS : a tribute to Helena Rasiowa Logic, Algebra and Computer Science. Helena Rasiowa A Minisemester at Warsaw, December 222, 1996. Mohua Banerjee Machine Intelligence Unit, Indian Statistical Institute, Calcutta E-mail: miux9503@isical.ernet.in The atmosphere was easy-unlike that in a standard conference-and the long span of the meeting gave one a lot of scope for academic interaction. Quite a few participants were close associates/students of Rasiowa, and so during conversations, one caught glimpses of the great personality as well. It was a privilege to be a part of the assembly and also, to present our work on rough logic that follows Rasiowa's style of investigation. The participants were accommodated either at the Banach Center, or hotels of the University of Warsaw, and the organizers took great care to see to the comfort of each one (in particular that none froze!). In general too, considering the extremely hard time that the Polish are going through, one was amazed at the warmth exuded and help extended, even by the common person on the street. Among the audience, we had a number of bright young students (Polish, and others), shooting questions, and enjoying the proceedings. I remember a nice evening with some of them, trudging through the ice to a concert at the renowned Chopin School of Music, and then being amply rewarded by the concert itself-three well-performed piano concertos by students of the School. We also had long exchanges about the problems in our countries, specially those in the academic spheres. There did not seem to be many differences.

74. Concurrency-1993: Algebraic And Categorical Methods In Computer Science Tempus Summer School for Algebraic and categorical Methods. in Computer Science. PJ Freyd (Philadelphia), Cartesian logic and Cartesian Categories. http://www-i2.informatik.rwth-aachen.de/Forschung/MCS/Mailing_List_archive/con_h

Algebraic and Categorical Methods in Computer Science Lubos Brim ( brim@adelard.dcs.muni.cs Thu, 6 May 1993 12:11:02 +0200 Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Bard Bloom: "CFP: North American Process Algebra Workshop" Previous message: Frits.Vaandrager@cwi.nl: "CF Participation PN93/Chicago, Final Prog" Tempus Summer School for Algebraic and Categorical Methods in Computer Science Second Announcement Brno, June 28 - July 3, 1993 Sponsored by the European Community TEMPUS office the organizers are pleased to announce an intensive course designed to serve its students as a forum for exchange of ideas between the disciplines of mathematics and computer science. Courses: P. J. Freyd (Philadelphia), Cartesian Logic and Cartesian Categories Y. Lafont (Paris), Linear Logic J. Lambek (Montreal), Categories and Deductive Systems C. P. Stirling (Edinburgh), Modal and Temporal Logics for Processes G. Winskel (Aarhus), Models and Logic for Concurrent Computation

75. Step By Step - Building Representations In Algebraic Logic Step by Step Building Representations in Algebraic logic We consider the problem of finding and classifying representations in algebraic logic. This is approached by letting two players build a http://rdre1.inktomi.com/click?u=http://citeseer.ist.psu.edu/259280.html&y=0

76. Non-Orthomodular Models For Both Quantum Logic And Standard Classical NonOrthomodular Models for Both Quantum logic and Standard Classical logic Repercussions for Quantum Computers It is shown that propositional calculuses of both quantum and classical logics are http://rdre1.inktomi.com/click?u=http://citebase.eprints.org/cgi-bin/citations?i

77. IEEE Symposium On Logic In Computer Science -- 1988 A categorical semantics of constructions. Complete axiomatizations of the algebras of finite, rational Proceedings, Third Annual Symposium on logic in Computer http://theory.lcs.mit.edu/~dmjones/LICS/lics88.html

IEEE Symposium on Logic in Computer Science 1988 Phokion G. Kolaitis and Moshe Y. Vardi . 0-1 laws and decision problems for fragments of second-order logic. In Proceedings, Third Annual Symposium on Logic in Computer Science , pages 2-11, Edinburgh, Scotland, 5-8 July 1988. IEEE Computer Society. References, Citations, etc. BibTeX entry Kevin L. Compton and Claude Laflamme . An algebra and a logic for NC ^1. In Proceedings, Third Annual Symposium on Logic in Computer Science , pages 12-21, Edinburgh, Scotland, 5-8 July 1988. IEEE Computer Society. References, Citations, etc. BibTeX entry M. Tiomkin . Proving unprovability. In Proceedings, Third Annual Symposium on Logic in Computer Science , pages 22-26, Edinburgh, Scotland, 5-8 July 1988. IEEE Computer Society. References. BibTeX entry C. A. R. Hoare and M. J. C. Gordon . Partial correctness of C-MOS switching circuits: An exercise in applied logic. In Proceedings, Third Annual Symposium on Logic in Computer Science , pages 28-36, Edinburgh, Scotland, 5-8 July 1988. IEEE Computer Society. [ BibTeX entry Kim B. Bruce

78. Elsevier Author Gateway Elsevier s Science of Computer Programming and Theoretical Computer Science by its focus on the foundations of logical, algebraic and categorical methods for http://authors.elsevier.com/JournalDetail.html?PubID=621520&Precis=DESC

79. Algebra General Logic Featured Books. logic as algebra logic as algebra This book reviews some ideas Halmos worked on in the 1950s the algebraization of predicate logic. http://mathematicsbooks.org/Algebra_General_Logic.html

Home Search High Volume Orders Links ... Philosophy of Mathematics Additional Subjects Fashion Illustration Now William Sleator Generals in Blue Lives of the Union Commanders: Lives of the Union Commanders Snakes of Georgia South Carolina ... The Call Goes Out: Interspecies Communication Featured Books This book is without peer in its breadth of coverage of the foundations of mathematics and logic. I have given this book only 4 stars, because its treatment of any given topicis not classic. It is the total package that astounds.For a mere $15, you get a challenging undergraduate introduction to all of the following topics. I have written in parentheses the names of authors of more definitive treatments:Intuitive set theory through the axiom of choice (Halmos)Natural numbers † Integers † Ra... Written by Robert R. Stoll Published by Dover Pubns (October 1979) ISBN 0486638294 Price $18.95 Communication Complexity Communication Complexity studies how many bits ALICE and BOB have to exchange to computer a function. Questinos of this sort are interesting in and of themselves AND also because they help proof lower Bounds on models of computation like circuits and decision trees. THIS book is readable and gives you all the basics that you need. The authors present clean proofs of basic theorems on how many bits are needed, and also supply links to other models nicely, and proof lower bounds on those models... Written by Eyal Kushilevitz Noam Nisan Published by Cambridge University Press (December 1996)

80. The Logic Of Bunched Implications 1. Introduction to Part I. 2. Natural Deduction for Propositional BI. 3. Algebraic, Topological, categorical. 8. Bunched Logical Relations. http://www.cs.bath.ac.uk/~pym/BI.html

The Logic of Bunched Implications We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication and can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI 's proofs are given by bicartesian doubly closed categories, i.e. , categories which freely combine the semantics of propositional intuitionistic logic and propositional multiplicative intuitionistic linear logic. The predicate version of BI includes, in addition to standard additive quantifiers, multiplicative (or intensional) quantifiers for all new and there exists new which arise from observing restrictions on structural rules on the level of terms as well as propositions. We discuss computational interpretations, based on sharing, at both the propositional and predicate levels. Basic References [1] P.W. O'Hearn and D.J. Pym

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