Intelligent Computer Mathematics

Thisvolumecontainsthecollectedcontributionsofthreeconferences,AISC2010, Calculemus 2010 and MKM 2010. AISC 2010 was the 10th International C- ference on Arti?cial Intelligence and symbolic computation. Its area of concern is the use of AI techniques within symbolic computation as well as the appli- tion of symbolic computation to AI problem solving. Calculemus 2010 was the 17th Symposium on the Integration of Symbolic Computation and Mechanised Reasoning, dedicated to the combination of computer algebra systems and - tomated deduction systems. MKM 2010 was the 9th International Conference on Mathematical KnowledgeManagement, an emerging interdisciplinary?eld of research in the intersection of mathematics, computer science, library science, andscienti?cpublishing. Allthreeconferencesarethusconcernedwithproviding intelligent computer mathematics. Although the conferences have separate c- munities and separate foci, there is a signi?cant overlap of interest in building systems for intelligent computer mathematics. As in 2008 and 2009,the three events were colocated. In 2010 this was at the Conservatoire National des Arts et M etiers (CNAM), Paris, France, under the umbrellaoftheConferencesonIntelligentComputerMathematics(CICM2010), organized by Renaud Rioboo and Laurence Rideau. This collocation is intended to counteract the tendency towards fragmentation of communities working on di?erent aspects of various independent branchesof our general?eld; traditional branches (e. g. , computer algebra, theorem proving and arti?cial intelligence in general), as well as newly emerging ones (on user interfaces, knowledge mana- ment, theory exploration, etc. ). This also facilitates the development of systems for intelligent computer mathematics that will be routinely used by mathema- cians, computer scientists and engineers in their every-day work.

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Klappentext

This book constitutes the joint refereed proceedings of the 10th International Conference on Artificial Intelligence and Symbolic Computation, AISC 2010, the 17th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2010, and the 9th International Conference on Mathematical Knowledge Management, MKM 2010. All submissions passed through a rigorous review process. From the 25 papers submitted to AISC 2010, 9 were selected for presentation at the conference and inclusion in the proceedings volume. A total of 14 papers were submitted to Calculemus, of which 7 were accepted. MKM 2010 received 27 submissions, of which 16 were accepted for presentation and publication. The events focused on the use of AI techniques within symbolic computation and the application of symbolic computation to AI problem solving; the combination of computer algebra systems and automated deduction systems; and mathematical knowledge management, respectively.

Inhalt
Contributions to AISC 2010.- The Challenges of Multivalued Functions.- The Dynamic Dictionary of Mathematical Functions.- A Revisited Perspective on Symbolic Mathematical Computing and Artificial Intelligence.- I-Terms in Ordered Resolution and Superposition Calculi: Retrieving Lost Completeness.- Structured Formal Development with Quotient Types in Isabelle/HOL.- Instantiation of SMT Problems Modulo Integers.- On Krawtchouk Transforms.- A Mathematical Model of the Competition between Acquired Immunity and Virus.- Some Notes upon When Does $]]> Equal Sat ?.- How to Correctly Prune Tropical Trees.- From Matrix Interpretations over the Rationals to Matrix Interpretations over the Naturals.- Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar.- Contributions to Calculemus 2010.- Some Considerations on the Usability of Interactive Provers.- Mechanized Mathematics.- Formal Proof of SCHUR Conjugate Function.- Symbolic Domain Decomposition.- A Formal Quantifier Elimination for Algebraically Closed Fields.- Computing in Coq with Infinite Algebraic Data Structures.- Formally Verified Conditions for Regularity of Interval Matrices.- Reducing Expression Size Using Rule-Based Integration.- A Unified Formal Description of Arithmetic and Set Theoretical Data Types.- Contributions to MKM 2010.- Against Rigor.- Smart Matching.- Electronic Geometry Textbook: A Geometric Textbook Knowledge Management System.- An OpenMath Content Dictionary for Tensor Concepts.- On Duplication in Mathematical Repositories.- Adapting Mathematical Domain Reasoners.- Integrating Multiple Sources to Answer Questions in Algebraic Topology.- An Integrated Development Environment for Collections.- Proofs, Proofs, Proofs, and Proofs.- Dimensions ofFormality: A Case Study for MKM in Software Engineering.- Towards MKM in the Large: Modular Representation and Scalable Software Architecture.- The Formulator MathML Editor Project: User-Friendly Authoring of Content Markup Documents.- Notations Around the World: Census and Exploitation.- Evidence Algorithm and System for Automated Deduction: A Retrospective View.- On Building a Knowledge Base for Stability Theory.- Proviola: A Tool for Proof Re-animation.- A Wiki for Mizar: Motivation, Considerations, and Initial Prototype.