Intelligent computer mathematics : 16th symposium, Calculemus 2009 ; 8th international conference, MKM 2009, held as part of CICM 2009, Grand Bend, Canada, July 6-12, 2009 ; proceedings

Annotation 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 Front Matter....Pages - Computational Logic and Continuous Mathematics, Pure and Applied....Pages 1-1 Math-Literate Computers....Pages 2-13 Abstraction-Based Information Technology: A Framework for Open Mechanized Reasoning....Pages 14-26 Software Engineering for Mathematics....Pages 27-27 Some Traditional Mathematical Knowledge Management....Pages 28-28 Math Handwriting Recognition in Windows 7 and Its Benefits....Pages 29-30 Assembling the Digital Mathematics Library....Pages 31-31 CAMAL 40 Years on – Is Small Still Beautiful?....Pages 32-44 Conservative Retractions of Propositional Logic Theories by Means of Boolean Derivatives: Theoretical Foundations....Pages 45-58 Combining Coq and Gappa for Certifying Floating-Point Programs....Pages 59-74 A Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy....Pages 75-89 Exploring a Quantum Theory with Graph Rewriting and Computer Algebra....Pages 90-105 ACL2 Verification of Simplicial Degeneracy Programs in the Kenzo System....Pages 106-121 Combined Decision Techniques for the Existential Theory of the Reals....Pages 122-137 Reasoning with Generic Cases in the Arithmetic of Abstract Matrices....Pages 138-153 Invariant Properties of Third-Order Non-hyperbolic Linear Partial Differential Operators....Pages 154-169 A Groupoid of Isomorphic Data Transformations....Pages 170-185 Algorithms for the Functional Decomposition of Laurent Polynomials....Pages 186-200 A Linear Grammar Approach to Mathematical Formula Recognition from PDF....Pages 201-216 Formal Proof: Reconciling Correctness and Understanding....Pages 217-232 A Review of Mathematical Knowledge Management....Pages 233-246 OpenMath Content Dictionaries for SI Quantities and Units....Pages 247-262 Unifying Math Ontologies: A Tale of Two Standards....Pages 263-278 Integrating Web Services into Active Mathematical Documents....Pages 279-293 Representation for Interactive Exercises....Pages 294-309 The Characteristics of Writing Environments for Mathematics: Behavioral Consequences and Implications for Software Design and Usability....Pages 310-324 Canonical Forms in Interactive Exercise Assistants....Pages 325-340 Spreadsheet Interaction with Frames: Exploring a Mathematical Practice....Pages 341-356 Compensating the Computational Bias of Spreadsheets with MKM Techniques....Pages 357-372 MathLang Translation to Isabelle Syntax....Pages 373-388 A Mathematical Approach to Ontology Authoring and Documentation....Pages 389-404 A Logically Saturated Extension of ${{\bar\lambda\mu\tilde{\mu}}}$ ....Pages 405-421 From Tessellations to Table Interpretation....Pages 422-437 Finite Groups Representation Theory with Coq ....Pages 438-452 Collaborative Assistant to Handle MathML Expressions....Pages 453-459 Confidence Measures in Recognizing Handwritten Mathematical Symbols....Pages 460-466 Using Open Mathematical Documents to Interface Computer Algebra and Proof Assistant Systems....Pages 467-473 OpenMath in SCIEnce: SCSCP and POPCORN....Pages 474-479 A Knowledge Repository for Indefinite Integration Based on Transformation Rules....Pages 480-485 Natural Deduction Environment for Matita....Pages 486-491 Back Matter....Pages - 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. This book constitutes the joint refereed proceedings of the 20th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2013, 6th International Workshop on Digital Mathematics Libraries, DML 2013, Systems and Projects, held in Bath, UK as part of CICM 2013, the Conferences on Intelligent Computer Mathematics. The 7 revised full papers out of 18 submissions for MKM 2013, 5 revised full papers out of 12 submissions for Calculemus 2013, 6 revised full papers out of 8 submissions for DML 2013, and 12 revised full papers out of 16 submissions for Systems and Project track presented together with 3 invited talks were carefully reviewed and selected, resulting in 33 papers from a total of 73 submissions.