21. On Specification Logics For Algebra-coalgebra Structures: Reconciling Reachabili Handbook of categorical algebra, volume 2. CUP, 1994. 5. C. C rstea. Coalgebraic logic. Annals of Pure and Applied logic, 96, 1999. 14. H. Reichel. http://eprints.ecs.soton.ac.uk/9116/

@import url(http://eprints.ecs.soton.ac.uk/style/auto.css); @import url(http://eprints.ecs.soton.ac.uk/style/print.css); @import url(http://eprints.ecs.soton.ac.uk/style/nojs.css); Site Search Home UG Study MSc Admissions PG Opportunities ... Intranet Breadcrumb trail: University of Southampton ECS Research Publications ... Browse by year Intranet Tools Add publications Modify RAE Information RSS 1.0 Feed RSS 2.0 Feed ... Atom Feed On specification logics for algebra-coalgebra structures: reconciling reachability and observability Cirstea, C. (2002) On specification logics for algebra-coalgebra structures: reconciling reachability and observability. In: Foundations of Software Science and Computation Structures Conference, 10-12 April 2002, Grenoble, France. Download Preview PDF - Requires a PDF viewer such as GSview Xpdf or Adobe Acrobat Reader 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.

22. Bulletin Of The American Mathematical Society MR 574645; * J. Lambek, On the unity of algebra and logic, F. Borceux (éd.), categorical algebra and its Applications, Lecture Notes in Math., vol. http://www.ams.org/bull/1989-21-02/S0273-0979-1989-15849-7/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1088-9485(e) ISSN 0273-0979(p) Previous issue Table of contents Next issue Articles in press ... Next Article Book Review The AMS does not provide abstracts of book reviews. You may download the entire review from the links below. Retrieve article in: PDF Book Information Author(s): J. L. Bell Title: Toposes and local set theories: An introduction Additional book information: Oxford Logic Guides: 14, Clarendon Press, Oxford, 1988, xii + 267 pp., $75.00. ISBN 0-19-853274-1 References: , Lecture Notes in Math., vol. 269, Springer-Verlag, Berlin and New York, 1972. M. Barr, Toposes without points , J. Pure Appl. Algebra 5 (1974), 265-280. MR A. Boileau and A. Joyal, La logique des topos , J. Symbolic Logic 46 (1981), 6-16. MR A. Church, A foundation of the simple theory of types , J. Symbolic Logic 5 (1940), 56-88. MR S. Eilenberg and S. Mac Lane, General theory of natural equivalences , Trans. Amer. Math. Soc. 58 (1945), 231-294.

23. Homepage For Prof. Erwin Engeler Author of various books on logic, Mathematics and Computer Science, translated into Russian, Japanese and categorical algebra, eds S. Eilenberg et al. http://www.math.ethz.ch/~engeler/

Prof. Erwin Engeler Curriculum Vitae: Dates and Stations Activities and Offices Publications Classical model theory and infinitary languages ... Miscellaneous My address: Department of Mathematics, HUT Federal Institute of Technology 8092 Zurich, Switzerland Phone: + 41 44 632 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

24. Salvador Vera: Directorio - Algebra categorical Geometry Homepage This site contains online books and research papers on the subjects of categorical algebra, categorical logic, categorical http://www.satd.uma.es/matap/svera/links/matnet01.html

Álgebra Restaurar marco Añade tu web Anterior Home ... Siguiente en todo el directorio Dmoz sólo en Matemáticas/Álgebra Top Directorio Español: Matemáticas Álgebra Descripción Genéricas: Acontecimientos Aplicaciones Asociaciones Bibliotecas ... Software Específicas: Álgebra Análisis An. Numérico Cálculo ... Álgebra lineal Esta categoría en otros idiomas: Inglés Álgebra abstracta - Conceptos generales de álgebra abstracta y lógica. Definiciones y teoremas. Estructuras algebraicas - Apuntes en pdf de un curso de Estructuras Algebraicas. Anillos, extensiones de cuerpos, la correspondencia de Galois, cuerpos finitos, raíces de la unidad, extensiones normales y trascendentes y otros temas. Vectores - Magnitud, suma y resta de vectores. Vectores en el plano - Contiene applets de Java. Algebra Algebraists Category Theory Group Theory High School Math ... Elements of Abstract and Linear Algebra, by Edwin H. Connell Full online book, in 4 formats: Abode Acrobat, DVI, Postscript, and gzipped Postscript. Can be read with Abode's free Acrobat Reader. Linear Algebra WebNotes by Dr. Mark Sapir

25. Publications Of David M Evans J. M. Larrazabal, D. Lascar, G. Mints, Lecture Notes in logic 12, pp 7999, zero categorical structures , in Advances in Model Theory and algebra, eds. http://www.mth.uea.ac.uk/~h120/publications.html

Research publications of David M Evans Papers by research students Slides of talks Reports on Grants The following list of papers is in approximate reverse chronological order. It also contains preprints, which can be downloaded in .pdf .dvi or .ps format. I have offprints of all of the published papers (with the possible exception of ones published in books). If you would like one, or a hard copy of a preprint, then let me know by e-mail. [38] "Expansions of fields by angular functions", to appear in proceedings of the conference 'Logicum Lugdunensis', revised version, September 2007 (.pdf) [37] (with Mark Wing Ho Wong) "Some remarks on generic structures", Preprint, August 2006 (.pdf) (Older version, July 2003 (.pdf) [36] "Block transitive Steiner systems with more than one point orbit", J. Combinatorial Designs 12 (2004), 459-465. (.pdf) [35] "Trivial stable structures with non-trivial reducts", J. London Math. Soc (2) 72 (2005), 351-363. (.pdf) [34] (with Paul R. Hewitt) "Continuous cohomology of permutation groups on profinite modules", Communications in Algebra 34 (2006), 1251 - 1264. (.pdf)

26. WORKSHOP Workshop. categorical Methods in algebra, Topology and logic Normal subobjects of topological groups and of topological semiabelian algebras http://www.mat.uc.pt/~categ/events/abril2005.html

Workshop Categorical Methods in Algebra, Topology and Logic April 8, 2005 A logic of coequations Jiri Adámek (Technical University of Braunschweig, Germany) On the construction of quasi-uniform structures in pointfree topology Maria João Ferreira (Universidade de Coimbra, Portugal) Coffee Break Axioms for sequential convergence Dirk Hofmann (Universidade de Aveiro, Portugal) April 15, 2005 Normal subobjects of topological groups and of topological semi-abelian algebras Dominique Bourn (Université du Littoral Côte d'Opale, France) Baer sums in Moore categories Diana Rodelo (Universidade do Algarve, Portugal) Coffee Break From bicategories and double categories to pseudo-categories: a generalization Nelson Martins-Ferreira (Instituto Politécnico de Leiria, Portugal) Representability of actions in the semi-abelian category of von Neumann regular rings Francis Borceux (Université Catholique de Louvain, Belgium) Room 5.5, Mathematics Department, University of Coimbra

27. ScienceDirect - Journal Of Pure And Applied Algebra : An Equational Variant Of L J. Lambek, On the unity of algebra and logic. In F. Borceux, Editor, categorical algebra and its Applications, Lecture Notes in Mathematics, vol. http://linkinghub.elsevier.com/retrieve/pii/S0022404999001784

Athens/Institution Login Not Registered? User Name: Password: Remember me on this computer Forgotten password? Home Browse My Settings ... Help Quick Search Title, abstract, keywords Author e.g. j s smith Journal/book title Volume Issue Page Journal of Pure and Applied Algebra Volume 154, Issues 1-3 , 1 December 2000, Pages 265-272 Abstract Full Text + Links PDF (76 K) Related Articles in ScienceDirect Contribution to the study of the natural number object ... Journal of Pure and Applied Algebra Contribution to the study of the natural number object in elementary Topoi Journal of Pure and Applied Algebra Volume 17, Issue 1 April 1980 Pages 35-68 Abstract Abstract + References PDF (1843 K) On natural number objects, finiteness and Kripke ... Journal of Pure and Applied Algebra On natural number objects, finiteness and Kripke Platek models in toposes Journal of Pure and Applied Algebra Volume 61, Issue 3 24 November 1989 Pages 257-266 Bruno Loiseau and Mawanda Mbila-Mambu Abstract Our aim is to show that if a topos has a natural number object, then this object N can be equipped with a binary structure which makes it a Kripke-Platek model. We first give some results concerning (Kuratowski-) finite parts of

28. Bilgi Mathematics Faculty: Prof. Oleg Belegradek Research areas algebra, mathematical logic and applications Almost categorical theories, Master Thesis, Novosibirsk State University, 1972. http://www.math.bilgi.edu.tr/people/belegradek/

Prof. Oleg Belegradek Ana sayfa / Home Biz kimiz? / About Us Aile bireyleri / People Tüm dersler / All Courses ecture Notes Set Theory: dvi pdf ps Algebra: dvi pdf ps Analysis: dvi pdf ps Takvim / Calendar 2003-2004 ... Poizat's Model Theory Book in Russian CURRICULUM VITAE for Oleg Belegradek Date of birth November 24, 1949 Place of birth Chelyabinsk, Russia Telephone +90 (212) 2162222/198 (office) +90 (212) 2168477 (fax) e-mail address: olegb@bilgi.edu.tr Degrees Doctor of Science (Mathematics), 1995, Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Novosibirsk Candidate of Science (Mathematics), 1975, Novosibirsk State University Master (Mathematics), 1972, Novosibirsk State University Research areas Algebra, mathematical logic and applications Academic career Kemerovo State University, Department of Mathematics, Section of Algebra and Geometry, 1975-1977: Assistant professor, 1977-1986: Chairman, 1987-1995: Docent, 1995-1999: Professor Istanbul Bilgi University, Department of Mathematics

29. Categories Home Page Recent advances in category theory and logic Applications of traces to algebra, analysis and categorical logic, A Fields Institute Sponsored Workshop. http://www.mta.ca/~cat-dist/

Categories List How to use the list Archives Moderator Conferences of interest ... Addresses - electronic and postal General, Seminar-related, and Local Sites Theory and Applications of Categories - refereed electronic journal. TeX Macros for diagrams Using the list: Articles for posting should be sent to categories@mta.ca Administrative items (subscriptions, address changes etc.) should be sent to categories-request@mta.ca Usually, items of this sort sent to `categories@mta.ca' will not be posted. Policy: The moderator will not modify articles except for minor typographical and formatting changes, therefore no offensive or defamatory material should be sent (it will be returned and not posted), and inflammatory posts are discouraged. Nevertheless, wide latitude for vigorous debate is allowed. Please do not send attachments, html or excessively long (greater than about 10K) postings. Postings with attachments will be discarded, any with html may be. Return to top. Archives M. Alsani has created a selected list of CT email, also sorted by thread, from August 1999 to February 2002 at http://north.ecc.edu/alsani/cat-dist2html/index.html

30. Handbook Of Categorical Algebra, Volume 3 The Handbook of categorical algebra is intended to give, accessible and extensive description of the internal logic of toposes, a very powerful tool. http://assets.cambridge.org/97805214/41803/description/9780521441803_description

Cambridge University Press 0521441803 - Handbook of Categorical Algebra, Volume 3 - by Francis Borceux Description More information Description

31. EpistemeLinks: Journals For Philosophy Of Mathematics The Annals of Pure and Applied logic publishes papers and short . that significantly advance the study of categorical algebra or methods,...... http://www.epistemelinks.com/Main/Journals.aspx?Format=Both&TopiCode=Math

32. Peter Selinger: Curriculum Vitae Invited participant, Special Session on categorical logic and Quantum Invited participant, Workshop on algebra and logic on Programming Systems, Kyoto, http://www.mathstat.dal.ca/~selinger/cv.html

C URRICULUM V ITAE - P ETER S ELINGER Updated: April 2007 P ERSONAL D ETAILS Address: Department of Mathematics and Statistics Dalhousie University Chase Building Halifax, Nova Scotia B3H 3J5, Canada Telephone: Office 902-494-3311 Fax 902-494-5130 E-mail: selinger@mathstat.dal.ca E DUCATION University of Pennsylvania, Philadelphia, U.S.A., 1992-1997. Ph.D. in Mathematics. Thesis Advisor: Andre Scedrov. Thesis Title: Functionality, Polymorphism, and Concurrency: A Mathematical Investigation of Programming Paradigms. Cambridge University, Cambridge, England. August-December 1995. Affiliated participant, Special Term on Semantics of Computation, Isaac Newton Institute for Mathematical Sciences. Technische Hochschule Darmstadt, Darmstadt, Germany. 1989-1992. Undergraduate studies in Mathematics, with minors in Computer Science and Theoretical Physics. E MPLOYMENT Associate Professor (tenured), Department of Mathematics and Statistics, Dalhousie University. 2005-present Adjunct Professor, Department of Mathematics and Statistics, University of Ottawa.

33. Atlas: Computable Isomorphisms Of Boolean Algebras With Operators By Bakhadyr M. For any natural number n there exists a computably categorical BAO B such that the Computable Univalent Numerations, algebra and logic 19, N 5, p. http://atlas-conferences.com/c/a/i/g/29.htm

Atlas home Conferences Abstracts about Atlas International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures May 21-24, 2002 Vanderbilt University Nashville, TN, USA Organizers Jonathan Farley, Ralph Freese, Matthew Gould, Peter Jipsen, George McNulty, Miklos Maroti, Alexander Ol'shanskii, Steven Tschantz, Constantine Tsinakis, Matthew Valeriote View Abstracts Conference Homepage Computable Isomorphisms of Boolean Algebras with Operators by Bakhadyr M. Khoussainov Computer Science Department, The University of Auckland, New Zealand. Coauthors: Tomasz Kowalski (JAIST, Japan) In computable algebra and model theory computable isomorphism types of structures have been studied intensively over almost three decades. These include a number of natural classes of structures, such as Boolean algebras, Abelian groups, and lattices. The Handbook of Recursive Mathematics is a good source of results in the area. Here we present two results about computable isomorphisms of Boolean algebras with operators (BAOs). A computable BAO A is one whose domain is a computable subset of N, and whose Boolean operations and the operators are computable functions. If a BAO

34. That Logic Blog: Meaning Via Proofs Now, suppose that we are working in classical logic and wish to assert some In the next post, I ll write a little about what categorical algebra has to http://thatlogicblog.blogspot.com/2006/07/meaning-via-proofs.html

@import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?targetBlogID=9821078"); That Logic Blog July 07, 2006 Meaning via Proofs Verificationism is the idea, popular amongst the logical positivists, that the meaning of a sentence is to be equated with the method used to establish it. That is, a statement is true if and only if we can, in principle, verify its truth or if it is analytic, which is to say that it is true by definition. This sort of explanation seems to give the impression that semantics precedes syntax invert this procedure. That is, suppose we already know Then constructed from the analytic statements via certain inference rules. In other words, what we have discovered is that our model of classical logic is nothing but the free boolean algebra generated by the analytic statements. But we can summarise the situation in a far more snappy manner: Verification is dual to construction An even more catchy war cry is: Models are dual to proofs.

35. Siris: On Tom's Algebra Of Logic On Tom s algebra of logic. I have noted previously that propositional logic can be seen as a special case of categorical syllogistics. http://branemrys.blogspot.com/2008/01/on-toms-algebra-of-logic.html

@import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?targetBlogID=7193878"); Siris A Golden Chain from Tar-Water to the Trinity, With Thoughts Relating to Philosophy, Christian Theology, and the Universe Generally SEIREN CHRUSEIEN KREMASANTES Just War and Soldiers A Poem Draft Seventh Day of the Month See You Next Year ... Predicate Quantity I do work in early modern philosophy, but I have an interest in just about everything. Siris Site Feed (Atom) Weblogs I View Regularly Caveats For a rough introduction to my philosophy of blogging, click here . I intend on this weblog at least to try to meet the standard of Teresita Gonzalez-Quevedo's Code of Amiability . I consider blogging to be a very informal type of publishing - like putting up thoughts on your door, with a note asking for comments, or like brainstorming sessions. Nothing in this weblog is done rigorously: it's a place for jottings and first impressions. Because I consider posts here to be 'literary seedings' rather than finished products, nothing here should be taken as if it were anything more than an attempt to rough out some basic thoughts on various issues. Learning to look at any topic philosophically requires, I think, jumping right in, even knowing that you might be making a fool of yourelf; so that's what I do. My primary interest in most topics is the flow and structure of reasoning they involve rather than their actual conclusions, so most of my posts are about that. If, however, you find me making a clear factual error, let me know; blogging is a great way to get rid of misconceptions.

36. ON SOME CATEGORICAL ALGEBRA ASPECTS OF AUTOMATA THEORY: THE CATEGORICAL PROPERTI categorical algebra methods are applied to the precise formulation of this problem of a particular study of perfect automata. (Author)(*MATHEMATICAL logic. http://stinet.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0

37. MATHEMATICAL STRUCTURES RESEARCH Handbook of categorical algebra 1Basic Category Theory. Notes on categorical logic. University of Cambridge Computer Laboratory, 1989 http://www.mmsysgrp.com/mathstrc.htm

CATEGORY THEORY and MATHEMATICAL STRUCTURES Research topics include mathematical models and theories in the empirical sciences, models and theories in mathematics, category theory, and the use of mathematical structures in theoretical computer science. Research Bibliography Mathematical Theories and Models Scientific Theories and Models Category Theory Theoretical Computer Science ... WWW Research Sites Mathematical Theories and Models Agazzi and Darvas. Philosophy of Mathematics Today. Kluwer Academic Publishers, 1997 Anglin and Lambek. The Heritage of Thales. Springer-Verlag, 1995 Akin, Ethan. The General Topology of Dynamical Systems. American Mathematical Society, 1993 Barwise, Jon. (ed) Handbook of Mathematical Logic. North-Holland,1977 Barwise, Jon. "Axioms for Abstract Model Theory" ,Annals of Mathematical Logic 7(1974) 221-265. Bell, John and Machover,Moshe. A Course in Mathematical Logic. North-Holland, 1977 Bridge, Jane. Beginning Model Theory. Clarendon Press, 1977 Burgess, John and Rosen, Gifeon. A Subject with No Object Oxford Press, 1997

38. Springer Online Reference Works A branch of mathematics dealing with the interaction between logic (cf. also Mathematical .. Appl. categorical algebra , Amer. Math. Soc. (1970) pp. 1–14 http://eom.springer.de/c/c120060.htm

Encyclopaedia of Mathematics C Article refers to Categorical logic A branch of mathematics dealing with the interaction between logic (cf. also Mathematical logic ) and category theory. Each of these disciplines has profoundly influenced the other. In fact, it may be claimed that, at a very basic level, logic and category theory are the same. At one time it was customary to divide logic into three parts: proof theory recursion theory and model theory . To all these, category theory can make some fundamental contributions. Logic has also been used for presenting the foundations of mathematics, and here too category theory has something to say. Categorical proof theory. One way of looking at proofs is to see them as deductions. A deduction is a method of inferring from (cf. also Derivation, logical Natural logical deduction ). Evidently, deducibility is reflexive and transitive, and this translates into the identity deduction and into composition of deductions Originally, logicians were not interested in asking when two deductions are equal; the first to do so was D. Prawitz

39. Heyting Algebra - Wikipedia, The Free Encyclopedia Heyting algebras arise as models of intuitionistic logic, a logic in which the law of . F. Borceux, Handbook of categorical algebra 3, In Encyclopedia of http://en.wikipedia.org/wiki/Heyting_algebra

Heyting algebra From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics Heyting algebras are special partially ordered sets that constitute a generalization of Boolean algebras . Heyting algebras arise as models of intuitionistic logic , a logic in which the law of excluded middle does not in general hold. Complete Heyting algebras are a central object of study in pointless topology Contents Formal definition Alternative definitions Lattice-theoretic definitions Bounded lattice with an implication operation ... edit Formal definition A Heyting algebra H is a bounded lattice such that for all a and b in H there is a greatest element x of H such that This element is the relative pseudo-complement of a with respect to b , and is denoted . We write 1 and for the largest and the smallest element of H , respectively. In any Heyting algebra, one defines the pseudo-complement of any element x by setting . By definition, , and is the largest element having this property. However, it is not in general true that , thus is only a pseudo-complement, not a true

40. Blogicum: Relational Categorical Propositions On algebra of logic 1 Multiple quantification Relational categorical propositions which may be considered a general form of relational categorical http://blogicum.blogspot.com/2007/12/relational-categorical-propositions.html

Blogicum Archive January Missing types 7 On algebra of logic 4 On algebra of logic 3 ... Missing types of categorical propositions 1 Resources Vatican NewAdvent EWTN CatholicCulture ... The Logic Museum Blogs I follow Siris Sacramentum Vitae pontifications Just Thomism ... Maverick Philosopher Feed Subscribe in a reader Sunday, December 16, 2007 Relational categorical propositions I know Sommers and Englebretsen and others have treated these matters, but I'd like to think it over myself. There are three reasons why term logic is regarded inadequate: 1. Inability to treat reflexive inferences, eg. (a) Everybody killed himself (b) Cato killed Cato (c) Someone killed Cato 2. Inability to treat propositions with multiple quantification, eg. (d) All horses are animals (e) All horses' heads are animals' heads 3. Inability to treat transitions between term logic and propositional logic, eg. (f) Every inhabitant of the island is either Asiatic or European (g) Either every inhabitant of the island is Asiatic or s/he is European Relational problems First and second problem belong both to relational difficulties. Normal logical form for (a) is

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