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Functional analysis --- Algebraic topology --- Model theory. --- Ordered sets. --- Global analysis (Mathematics) --- Théorie des modèles --- Ensembles ordonnés --- Analyse globale (Mathématiques) --- 51 <082.1> --- Mathematics--Series --- Théorie des modèles --- Ensembles ordonnés --- Analyse globale (Mathématiques) --- Model theory --- Ordered sets --- Sets, Ordered --- Set theory --- Logic, Symbolic and mathematical --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.

Categories (Mathematics). --- Model theory. --- Representations of categories. --- Toposes. --- Categories (Mathematics) --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- Algebra, Homological. --- Homological algebra --- Category theory (Mathematics) --- Mathematics. --- Category theory (Mathematics). --- Homological algebra. --- Topology. --- Algebraic topology. --- Category Theory, Homological Algebra. --- Algebraic Topology. --- Algebra, Abstract --- Homology theory --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Algebra. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Mathematical analysis

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This volume contains the research papers presented at the 17th International Conference on Logic for Programming, Arti?cial Intelligence, and Reasoning (LPAR-17), held in Yogyakarta, Indonesia, October 10-15, 2010, accompanied by the 8th International Workshop on the Implementation of Logic (IWIL-8, organized by Eugenia Ternovska, Stephan Schulz, and Geo? Sutcli?e) and the 5th International Workshop on Analytic Proof Systems (APS-5, organized by Matthias Baaz and Christian Fermuller ¨ ). The call for papers attracted 133 abstract submissions of which 105 ma- rialized into full submissions, each of which was assigned for reviewing to at least three Program Committee members; 41 papers were accepted after - tense discussions. Once more the EasyChair system provided an ideal platform for submission, reviewing, discussions, and collecting ?nal versions of accepted papers. The program included three invited talks by Krishnendu Chatterjee, Joseph Halpern, and Michael Maher, as well as an invited tutorial by Norbert Preining. They are documented by the corresponding papers and abstract, respectively, in these proceedings, which this year appear for the ?rst time in the ARCoSS subline of the Lecture Notes in Computer Science.

Computer Science. --- Artificial Intelligence (incl. Robotics). --- Software Engineering. --- Logics and Meanings of Programs. --- Mathematical Logic and Formal Languages. --- Programming Techniques. --- Programming Languages, Compilers, Interpreters. --- Computer science. --- Software engineering. --- Logic design. --- Artificial intelligence. --- Informatique --- Génie logiciel --- Structure logique --- Intelligence artificielle --- Artificial intelligence --- Automatic theorem proving --- Logic programming --- 681.3*D24 --- 681.3*F3 --- 681.3*F41 --- 681.3*I23 --- Computer programming --- Automated theorem proving --- Theorem proving, Automated --- Theorem proving, Automatic --- Proof theory --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Program verification: assertion checkers; correctness proofs; reliability; validation (Software engineering)--See also {681.3*F31} --- Logics and meanings of programs (Theory of computation) --- Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*F41 Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- 681.3*F3 Logics and meanings of programs (Theory of computation) --- 681.3*D24 Program verification: assertion checkers; correctness proofs; reliability; validation (Software engineering)--See also {681.3*F31}