Intelligent Computer Mathematics

As computers and communications technology advance, greater opportunities arise for intelligent mathematical computation. While computer algebra, au- mated deduction and mathematical publishing each have long and successful histories, we are now seeing increasing opportunities for synergy among them. The Conferences on Intelligent Computer Mathematics (cicm 2009) is a c- lection of co-located meetings, allowing researchers and practitioners active in these related areas to share recent results and identify the next challenges. The speci?c areas of the cicm conferences and workshops are described below, but the unifying theme is the computerized handling of mathematical knowledge. The successful formalization of much of mathematics, as well as a better - derstanding of its internal structure, makes mathematical knowledge in many waysmore tractable than generalknowledge,as traditionally treatedin arti?cial intelligence. Similarly, we can also expect the problem of e?ectively using ma- ematical knowledge in automated ways to be much more tractable. This is the goal of the work in the cicm conferences and workshops. In the long view, so- ing the problems addressed by cicm is an important milestone in formulating the next generation of mathematical software.

Klappentext

This book constitutes the joint refereed proceedings of the 16th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2009 and the 8th International Conference on Mathematical Knowledge Management, MKM 2009, held in Grand Bend, Canada, as CICM 2009, the Conferences on Intelligent Computer Mathematics.

The 10 revised full papers and 4 invited talks for Calculemus 2009 and 16 revised full papers and 6 short communications for MKM 2009 presented together with 4 joint invited talks were carefully reviewed and selected from a total of 51 submissions. The papers of Calculemus 2009 cover all aspects of the interplay of mechanized reasoning and computer algebra, as well as the development of integrated systems that transcend both computer algebra and theorem proving. The focus of MKM 2009 lies at the intersection of mathematics and computer science with the goal of developing effective techniques, based on formal mathematics and software technology. The realm of mathematical information is an attractive candidate for testing innovative theoretical and technological solutions for content-based systems, interoperability, management of machine understandable information, and the semantic Web.

Inhalt
Joint Invited Talks.- Computational Logic and Continuous Mathematics, Pure and Applied.- Math-Literate Computers.- Abstraction-Based Information Technology: A Framework for Open Mechanized Reasoning.- Software Engineering for Mathematics.- Calculemus Talks.- Some Traditional Mathematical Knowledge Management.- Math Handwriting Recognition in Windows 7 and Its Benefits.- Assembling the Digital Mathematics Library.- CAMAL 40 Years on Is Small Still Beautiful?.- Conservative Retractions of Propositional Logic Theories by Means of Boolean Derivatives: Theoretical Foundations.- Combining Coq and Gappa for Certifying Floating-Point Programs.- A Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy.- Exploring a Quantum Theory with Graph Rewriting and Computer Algebra.- ACL2 Verification of Simplicial Degeneracy Programs in the Kenzo System.- Combined Decision Techniques for the Existential Theory of the Reals.- Reasoning with Generic Cases in the Arithmetic of Abstract Matrices.- Invariant Properties of Third-Order Non-hyperbolic Linear Partial Differential Operators.- A Groupoid of Isomorphic Data Transformations.- Algorithms for the Functional Decomposition of Laurent Polynomials.- MKM Talks.- A Linear Grammar Approach to Mathematical Formula Recognition from PDF.- Formal Proof: Reconciling Correctness and Understanding.- A Review of Mathematical Knowledge Management.- OpenMath Content Dictionaries for SI Quantities and Units.- Unifying Math Ontologies: A Tale of Two Standards.- Integrating Web Services into Active Mathematical Documents.- Representation for Interactive Exercises.- The Characteristics of Writing Environments for Mathematics: Behavioral Consequences and Implications for Software Design and Usability.- Canonical Forms inInteractive Exercise Assistants.- Spreadsheet Interaction with Frames: Exploring a Mathematical Practice.- Compensating the Computational Bias of Spreadsheets with MKM Techniques.- MathLang Translation to Isabelle Syntax.- A Mathematical Approach to Ontology Authoring and Documentation.- A Logically Saturated Extension of .- From Tessellations to Table Interpretation.- Finite Groups Representation Theory with Coq.- Collaborative Assistant to Handle MathML Expressions.- Confidence Measures in Recognizing Handwritten Mathematical Symbols.- Using Open Mathematical Documents to Interface Computer Algebra and Proof Assistant Systems.- OpenMath in SCIEnce: SCSCP and POPCORN.- A Knowledge Repository for Indefinite Integration Based on Transformation Rules.- Natural Deduction Environment for Matita.