1. Categorical Logic Lambek, J. and Scott, P. Introduction to HigherOrder categorical logic. Borceux, F. Handbook of categorical algebra (Encyclopedia of Mathematics and http://www.andrew.cmu.edu/~awodey/catlog/

Categorical Logic Fall 2006 Course Information Place: PH 226B Time: TTh 3 - 4:20 Instructor: Steve Awodey Office: Baker 152 (mail: Baker 135) Office Hour: Friday 1-2, or by appointment Phone: 8947 Email: awodey@andrew Secretary: Baker 135 Overview This course focuses on applications of category theory in logic and computer science. A leading idea is functorial semantics, according to which a model of a logical theory is a set-valued functor on a structured category determined by the theory. This gives rise to a syntax-invariant notion of a theory and introduces many algebraic methods into logic, leading naturally to the universal and other general models that distinguish functorial from classical semantics. Such categorical models occur, for example, in denotational semantics. In this connection the lambda-calculus is treated via the theory of cartesian closed categories. Similarly higher-order logic is modelled by the categorical notion of a topos. Using sheaves, topos theory also subsumes Kripke semantics for intuitionistic logic. Prerequisites 80-413/713 Category Theory, or equivalent.

2. George Voutsadakis nClosure Systems and n-Closure Operators, algebra Universalis, 55 (2006), 369-386 pdf; categorical Abstract algebraic logic Leibniz Equality and http://voutsadakis.com/RESEARCH/papers.html

George Voutsadakis Assistant Professor (with Tenure) School of Mathematics and Computer Science Lake Superior State University (On leave Spring 2008-Spring 2009, Department of Computer Science, Iowa State University) Research Interests Algebraic Logic Categorical and Universal Algebra Ordered Structures Combinatorics Theoretical Computer Science Mathematical Genealogy Technical Reports On Some Operations on Classes of Algebras and Coalgebras from a Bialgebraic Viewpoint pdf or postscript Probablistic Threshold Agent Networks pdf or postscript On the Categorical Mobius Calculus pdf or postscript Universal Bialgebra: Unifying Universal Algebra and Coalgebra pdf or postscript Combinatorial Analysis of the State Space Structure of Finite Automata Networks pdf or postscript Preprints Algebraic Logic Categorical Abstract Algebraic Logic: Tarski Congruence Systems, Logical Morphisms and Logical Quotients pdf or postscript Categorical Abstract Algebraic Logic: Generalized Tarski Congruence Systems pdf or postscript Categorical Abstract Algebraic Logic: Operations on Classes of Models pdf or postscript Categorical Abstract Algebraic Logic: Weakly Algebraizable pi-Institutions pdf or postscript Categorical Abstract Algebraic Logic: Closure Operators on Classes of PoFunctors pdf or postscript Categorical Abstract Algebraic Logic: Protoalgebraic Classes of Structure Systems pdf or postscript Categorical Abstract Algebraic Logic: Subdirect Representation for Classes of Structure Systems pdf or postscript Categorical Abstract Algebraic Logic: Selfextensional pi-Institutions with Implication

3. Review Saunders Mac Lane, Categorical Algebra And Set-Theoretic Review Saunders Mac Lane, categorical algebra and SetTheoretic Foundations. William Mitchell. Source J. Symbolic logic Volume 38, Issue 3 (1973), 528. http://projecteuclid.org/handle/euclid.jsl/1183738793

Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next Review: Saunders Mac Lane, Categorical Algebra and Set-Theoretic Foundations William Mitchell Source: J. Symbolic Logic Volume 38, Issue 3 (1973), 528. Reviewed Works: Saunders Mac Lane, Categorical Algebra and Set-Theoretic Foundations. Full-text: Remote access If you are a member of the ASL, log in to Euclid for access. Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR. Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.jsl/1183738793 JSTOR: links.jstor.org back to Table of Contents previous next Journal of Symbolic Logic Current Issue All Issues Search this Journal Editorial Board ... Log in RSS Cornell University Library

4. Universal Algebra And Logic Abstract algebra and logic are closely related and often mutually .. talks is to propose and study an order theoretic and categorical framework for the http://www.math.vanderbilt.edu/~ual/semi.html

5. Categorical Logic - Pitts (ResearchIndex) categorical logic. In Handbook of Theoretical Computer Science. Elsevier Science, 199? to . 1 the unity of algebra and logic (context) Lambek - 1988 http://citeseer.ist.psu.edu/pitts01categorical.html

6. Chronological List Of Publications categorical algebra for continuum microphysics, Journal of Pure and Applied algebra 175, (2002), 267287. 45. Metric Spaces, Generalized logic, http://www.buffalo.edu/~wlawvere/list.html

F. William Lawvere Chronological list of publications Home Subject Classification Bottom of page (most recent) 1. Functorial Semantics of Algebraic Theories Proceedings of the National Academy of Science 50 , No. 5 (November 1963), 869-872. 2. Elementary Theory of the Category of Sets Proceedings of the National Academy of Science 52 , No. 6 (December 1964), 1506-1511. Algebraic Theories, Algebraic Categories, and Algebraic Functors, Theory of Models ; North-Holland, Amsterdam (1965), 413-418. Functorial Semantics of Elementary Theories Journal of Symbolic Logic , Abstract, Vol. 31 (1966), 294-295. The Category of Categories as a Foundation for Mathematics La Jolla Conference on Categorical Algebra , Springer-Verlag (1966), 1-20. Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories Springer Lecture Notes in Mathematics No. 61 , Springer-Verlag (1968), 41-61. Ordinal Sums and Equational Doctrines Springer Lecture Notes in Mathematics No. 80 , Springer-Verlag (1969), 141-155. Diagonal Arguments and Cartesian Closed Categories Springer Lecture Notes in Mathematics No. 92

7. Applied Categorical Structures - Mathematical Logic And Foundations Journals, Bo Applied categorical Structures. A Journal Devoted to Applications of categorical Methods in algebra, Analysis, Order, Topology and Computer Science http://www.springer.com/west/home/math?SGWID=4-10042-70-35542984-0

8. BIBLIOGRAPHY About DESCENT And CATEGORY THEORY! \ 1348 \yr 1988; \bysame \book Handbook of categorical algebra 1 Basic . G. Reyes \book First Order categorical logic ModelTheoretical Methods in http://north.ecc.edu/alsani/catbib.html

BIBLIOGRAPHY about DESCENT THEORY from W. Tholen home page. Monades et Descente Selected Topics in Algebra An Outline of a Theory of Higher Dimensional Descent The Theory of Descent Triples and Descent An Extension of the Galois Theory of Grothendieck Theory of Categories over a Base Topos Descent Theory for Toposes Effective Descent Morphisms and Effective Equivalence Relations Introduction to Affine Group Schemes BIBLIOGRAPHY about CATEGORY THEORY F. W. Lawvere publications: http://www.acsu.buffalo.edu/~wlawvere Back to Descent and Category Theory WebPage Back to Alsani's home page

9. The Category Theoretic Understanding Of Universal Algebra Conf. on categorical algebra at La Jolla (1966), 336344. 2 Barr, M. and Wells, C., 32 Makkai, M. and Reyes, G., FirstOrder categorical logic. http://portal.acm.org/citation.cfm?id=1230590

10. IngentaConnect Categorical Abstract Algebraic Logic: Algebraizable Institutions categorical Abstract algebraic logic algebraizable Institutions are made precise using the theory of monads from categorical algebra and the notion of http://www.ingentaconnect.com/content/klu/apcs/2002/00000010/00000006/05090913

Home About Ingenta Ingenta Labs Ingenta Blog ... Check our FAQs Or contact us to report problems with: Subscription access Article delivery Registration Library administrator tasks ... Other problems For Publishers Why go online? Why choose IngentaConnect? Beyond Print: enhancing your service Access and authentication ... Contact us For Researchers For Authors About IngentaConnect Search and browse Publications available ... Register For Librarians Resource Zone Why choose IngentaConnect? Why choose IngentaConnect Complete? Activating Subscriptions ... Register CM8ShowAd("HorizontalBanner"); Categorical Abstract Algebraic Logic: Algebraizable Institutions Author: Voutsadakis G. Source: Applied Categorical Structures , Volume 10, Number 6, December 2002 , pp. 531-568(38) Publisher: Springer view table of contents Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Abstract: The framework developed by Blok and Pigozzi for the algebraizability of deductive systems is extended to cover the algebraizability of multisignature logics with quantifiers. Institutions are used as the supporting structure in place of deductive systems. In particular, the concept of an algebraic institution and that of an algebraizable institution are made precise using the theory of monads from categorical algebra and the notion of equivalence of institutions introduced by Voutsadakis. Several examples of algebraic and algebraizable institutions are provided.

11. PUT Libary March 2007 Borceux, Francis, Handbook of categorical algebra Vol. 1 Basic Category Theory Jacobs, Bart, categorical logic and Type Theory (paperback), 2001, Uwe http://www.ii.uib.no/~wolter/put/put-library.html

PUT Libary March 2007 Nr. Authors/Editors Title Year Place Abramsky/ Gabbay/ Maibaum Handbook of Logic in Computer Science Vol. 1 - Background: Mathematical Structures Uwe Abramsky/ Gabbay/ Maibaum Handbook of Logic in Computer Science Vol. 2 - Background: Computational Structures Michal Abramsky/ Gabbay/ Maibaum Handbook of Logic in Computer Science Vol. 4 - Semantic Modelling Michal Abramsky/ Gabbay/ Maibaum Handbook of Logic in Computer Science Vol. 5 - Logic and Algebraic Methods Michal Gabbay/Guenther Handbook of Philosophical Logic, 2nd Ed., Vol. 1 Michal Gabbay/Guenther Handbook of Philosophical Logic, 2nd Ed., Vol. 2 Michal Gabbay/Guenther Handbook of Philosophical Logic, 2nd Ed., Vol. 3 Michal Gabbay/Guenther Handbook of Philosophical Logic, 2nd Ed., Vol. 4 Michal Gabbay/Guenther Handbook of Philosophical Logic, 2nd Ed., Vol. 5 Michal Gabbay/Guenther Handbook of Philosophical Logic, 2nd Ed., Vol. 6 Michal Gabbay/Guenther Handbook of Philosophical Logic, 2nd Ed., Vol. 7 Michal Gabbay/Guenther Handbook of Philosophical Logic, 2nd Ed., Vol. 8

12. TUD : ACTUAL RESEARCH REPORT - Group 1. Algebra And Logic - Mathematical Logic A algebra and logic Mathematical logic and Foundations of Computer Science categorical logic, universal algebra, domain theory, lattice theory, http://www.tu-darmstadt.de/forschung/bericht/040100.en.tud

ACTUAL RESEARCH REPORT Group 1. Algebra and Logic - Mathematical Logic and Foundations of Computer Science Foreword by the President Tips for users Departments of the TUD Collaborative research centers ... Research homepage Full text search: Quick search in research report Advanced search in research report Advanced search in bibliography Contact: Arbeitsgruppe 1, Fachbereich Mathematik, Technische Universität Schlossgartenstraße 7 64289 Darmstadt Tel.: +49-6151-16-4686 Fax: +49-6151-16-3317 Building/Room: S2 15 / 206 E-mail: Internet: www.mathematik.tu-darmstadt.de/ags/ag1/Sekretariat/sekretariat_de.html Description of the Institute: Algebra and Logic - Mathematical Logic and Foundations of Computer Science Faculty: Ulrich Kohlenbach Martin Otto Thomas Streicher; Christian Herrmann ... Thomas Ihringer Retired: Peter Burmeister Klaus Keimel Rudolf Wille The research group primarily represents the subject area of Mathematical Logic viewed as an applied foundational discipline between mathematics and computer science . Research activities focus on the application of proof theoretic, recursion theoretic, category theoretic, algebraic and model theoretic methods from mathematical logic to mathematics and computer science. Beside classical mathematical logic (with proof theory, recursion theory and model theory) this involves constructive type theory, categorical logic, universal algebra, domain theory, lattice theory, finite model theory, and algorithmic issues.

13. JSTOR Categorical Algebra And Set-Theoretic Foundations. categorical algebra and SetTheoretic Foundations. William Mitchell. The Journal of Symbolic logic, Vol. 38, No. 3, 528. Dec., 1973. SAUNDERS MAC LANE. http://links.jstor.org/sici?sici=0022-4812(197312)38:3<528:CAASF>2.0.CO;2-B

14. Citebase - From Proof Nets To The Free *-Autonomous Category In Aldo Ursini and Paolo Agliano, editors, logic and algebra. Introduction to higher order categorical logic, volume 7 of Cambridge studies in advanced http://www.citebase.org/abstract?identifier=oai:arXiv.org:cs/0605054&action=cite

15. COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS - Cogprints random networks and Boolean algebra; Lukasiewics logic algebra isomporphic . categorical algebraLa Jolla. 1965, Eilenberg, S., et al. eds., Berlin, http://cogprints.org/3718/

@import url(http://cogprints.org/style/auto.css); @import url(http://cogprints.org/style/print.css); @import url(http://cogprints.org/style/nojs.css); Cogprints Home About Browse by Year ... Create Account COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS Baianu, Professor I.C. and Lin, Ms. H.C. COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS. [Book Chapter] Full text available as: Preview PDF - Requires a PDF viewer such as GSview Xpdf or Adobe Acrobat Reader Abstract Item Type: Book Chapter Additional Information: This updated paper addresses recent developments in quantum computation models of cognitive processes in the brain as well as in genetic networks, based on QMV- Logic and Lukasiewicz Logic Algebras (LLA)on the basis of the original published section that raised the question of biomimetics, or simulation of biosystems beyond recursive computation-based modeling, by means of n-valued logic, Quantum Computation, Quantum Automata and algebraic-topological symbolic models of both neural and genetic networks with very large numbers of components and complex, hierarchically organized brain structures. Keywords: Cognitive Neural Networks simulation by quantum computers; algebraic-topological, symbolic computation; Genetic Networks/Genome; Interactome simulations by computers; Recursive and digital computability limitations for biological and chaotic dynamics simulations;Kauffman, random networks and Boolean algebra; Lukasiewics Logic Algebra isomporphic to MV-logic algebra as model of biological system networks; Quantum MV-Logic algebras for microphysical modelling in Quantum Genetics and Enzyme Kinetics; Categories, functors, natural transformations and Topos as adequate tools for modelling hierarchical organization in biological systems and especially super-structures involved in cognitive processes supported by multi-layered neural networks.

16. Hidden Algebra Shows how to combine the logic and object paradigms using hidden algebra with . A categorical Manifesto, in Mathematical Structures in Computer Science, http://www.cs.ucsd.edu/~goguen/projs/halg.html

Hidden Algebra Homepage Contents Brief Overview Latest Hidden Results Brief Hidden Bibliography Interactive Examples ... Other Links A Brief Overview of Hidden Algebra Hidden algebra aims to give a semantics for software engineering, and in particular for concurrent distributed object systems, supporting correctness proofs that are as simple and mechanized as possible. This emphasis on effective proofs rather than semantic modelling is supported by taking a calculational approach based on equations , rather than one based on, for example, higher order logic, type theory, denotational semantics, or any particular kind of model or set theory, because equational proofs achieve maximal simplicity and mechanization, while still allowing adequate expressiveness. It is also convenient that the models of a hidden algebraic specification are precisely its possible implementations. Hidden algebra effectively handles the most troubling features of large systems, including concurrency, distribution, nondeterminism, and local states, as well as the usual features of the object paradigm, including classes, subclasses (inheritance), attributes and methods, in addition to supporting logical variables (as in logic programming), abstract data types, generic modules and more generally, the very powerful module system of prameterized programming. Hidden algebra generalizes the process algebra and transition system approaches to include non-monadic operations, so that it can take advantage of equations involving methods and attributes parameterized by data; this extra power can also dramatically simplify proofs. Coinduction methods appear to be more effective for behavioral properties (including behavioral refinement) than any alternative of which we are aware, and moreover, they can be automated to a very significant degree.

17. Publications, Lecture Notes Etc. - Thomas Streicher Allgemeine algebra für Informatiker und Wirtschaftsinformatiker (in German Category Theory and categorical logic pdf.gz. lecture notes for courses in http://www.mathematik.tu-darmstadt.de/~streicher/

Publications, Lecture Notes and some Unpublished Notes Publications Semantics of Type Theory. in the series Progress in Theoretical Computer Science. Basel: Birkhaeuser Verlag. XII, 298 p. (1991). Dependence and independence results for (impredicative) calculi of dependent types. Math. Struct. Comput. Sci. 2, No.1, 29-54 (1992). Independence of the induction principle and the axiom of choice in the pure calculus of constructions. Theor. Comput. Sci. 103, No.2, 395-408 (1992). Math. Struct. Comput. Sci. 4, No.1, 111-115 (1994). Investigations into Intensional Type Theory. This is a scanned version of my Habilitation Thesis from 1993. Here one can find models of intensional type theory refuting most of those judgements which trivially hold in extensional type theory but can't be proved in intensional type theory. In today's speak the most useful model (of Chapter 3) is obtained by glueing the global sections functor of the category of assemblies. pdf The groupoid interpretation of type theory with M. Hofmann

18. CATEGORICAL STRUCTURES AND THEIR APPLICATIONS The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy http://www.worldscibooks.com/mathematics/5665.html

Home Browse by Subject Bestsellers New Titles ... Browse all Subjects Search Bookshop New Titles Editor's Choice Bestsellers Book Series ... Join Our Mailing List CATEGORICAL STRUCTURES AND THEIR APPLICATIONS Proceedings of the North-West European Category Seminar Berlin, Germany 28 - 29 March 2003 edited by (Freie Universität Berlin, Germany) The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich — one of the leading category theorists of the world — to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader will find a complete list of Horst Herrlich’s publications. The proceedings have been selected for coverage in: Contents: On Boole’s Booleanness (B Banaschewski) The Tensor Product of Orthomodular Posets (R Börger) Saturated Collections of Metrics (E Colebunders et al.)

19. Algebra I Logika Complexity of categorical Theories with Computable Models English version algebra and logic, 2004, 436, 365–373 Review databases http://www.mathnet.ru/eng/al101

RUS ENG JOURNALS PERSONS ... LIBRARY var EDIT_DISABLED_BOOL; var CALENDAR_LANG; General information Latest issue Archive Search ... What is RSS Algebra Logika: Year: Volume: Issue: Page: Find Personal entry: Login: Password: Save password Enter Forgotten password? Register Algebra Logika, 2004, Volume 43 Number 6 (Mi al101) This paper is cited in scientific articles by authors PDF version HTML version Complexity of Categorical Theories with Computable Models S. S. Goncharov a B. Khoussainov b a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk b University of Auckland Abstract: M. Lerman and J. Scmerl specified some sufficient conditions for computable models of countably categorical arithmetical theories to exist. More precisely, it was shown that if $T$ is a countably categorical arithmetical theory, and the set of its sentences beginning with an existential quantifier and having at most $n+1$ alternations of quantifiers is for any $n$ , then $T$ has a computable model. J. Night improved this result by allowing certain uniformity and omitting the requirement that $T$ is arithmetical. However, all of the known examples of theories of

20. Curriculum Vitae Courses taught Abstract algebra, Introduction to Mathematical logic. . A categorical equivalence for integral GMValgebras, Workshop on algebra and http://www.jaist.ac.jp/~galatos/CV.html

Curriculum Vitae NIKOLAOS GALATOS School of Information Science Japan Advanced Institute of Science and Technology (JAIST) Asahidai, Nomi Ishikawa 923-1292, Japan Telephone: (+81) Fax: (+81) 761-51-1149 E-mail: galatos@jaist.ac.jp URL: http://www.jaist.ac.jp/~galatos Education Ph.D. in Mathematics, Vanderbilt University, Nashville, TN, USA, May 2003. Advisor: Professor Constantine Tsinakis. M.S. in Mathematics, Vanderbilt University, Nashville, TN, USA, May 2000. Advisor: Professor Constantine Tsinakis. Diploma (B.S.) in Mathematics, summa cum laude , Aristotle University, Thessaloniki, Greece, June 1998. Professional Experience Assistant Professor, Japan Advanced Institute of Science and Technology, since 2005. Assistant Professor, Vanderbilt University, 2004-2005. Postdoctoral Researcher, Japan Advanced Institute of Science and Technology, 2003-2004. Teaching Assistant, Vanderbilt University, 1998-2003. Teaching Experience Assisting with the supervision of Master’s and Ph.D. students, JAIST, since 2005. Seminar organizer, School of Information Science, JAIST, since 2005.

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