Towards Mechanized Mathematical Assistants: 14th Symposium, Calculemus 2007, 6th International Conference, MKM 2007, Hagenberg, Austria, June 27-30, 2007. Proceedings

Mirian Andrés, Laureano Lambán, Julio Rubio (auth.), Manuel Kauers, Manfred Kerber, Robert Miner, Wolfgang Windsteiger (eds.)3540730834, 9783540730835, 9783540730866

This volume contains the collected contributions of two conferences, Calcu- mus2007andMKM2007.Calculemus2007wasthe14thinaseriesofconferences dedicated to the integration of computer algebra systems (CAS) and automated deduction systems (ADS). MKM 2007 was the sixth International Conference on Mathematical Knowledge Management, an emerging interdisciplinary ?eld of research in the intersection of mathematics, computer science, library s- ence, and scienti?c publishing. Both conferences aimed to provide mechanized mathematical assistants. Although the two conferences have separate communities and separate foci, there is a signi?cant overlap in the interests in building mechanized mathem- ical assistants. For this reason it was decided to collocate the two events in 2007 for the ?rst time, at RISC in Hagenberg, Austria. The number and quality of the submissions show that this was a good decision. While the proceedings are shared, the submission process was separate. The responsibility for acc- tance/rejection rests completely with the two separate Program Committees. By this collocation we made a contribution against the fragmentation of communities which work on di?erent aspects of di?erent independent branches, traditional branches (e.g., computer algebra and theorem proving), as well as newly emerging ones (on user interfaces, knowledge management, theory exp- ration, etc.). This will also facilitate the development of integrated mechanized mathematical assistants that will be routinely used by mathematicians, c- puter scientists, and engineers in their every-day business.

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Table of contents :
Front Matter….Pages –
Executing in Common Lisp, Proving in ACL2….Pages 1-12
A Rational Reconstruction of a System for Experimental Mathematics….Pages 13-26
Context Aware Calculation and Deduction….Pages 27-39
Towards Constructive Homological Algebra in Type Theory….Pages 40-54
What Might “Understand a Function” Mean?….Pages 55-65
Biform Theories in Chiron….Pages 66-79
Automatic Synthesis of Decision Procedures: A Case Study of Ground and Linear Arithmetic….Pages 80-93
Certified Computer Algebra on Top of an Interactive Theorem Prover….Pages 94-105
Quantifier Elimination for Approximate Factorization of Linear Partial Differential Operators….Pages 106-115
Rule-Based Simplification in Vector-Product Spaces….Pages 116-127
Mathematics and Scientific Markup….Pages 128-129
The On-Line Encyclopedia of Integer Sequences….Pages 130-130
First Steps on Using OpenMath to Add Proving Capabilities to Standard Dynamic Geometry Systems….Pages 131-145
Higher order Proof Reconstruction from Paramodulation-Based Refutations: The Unit Equality Case….Pages 146-160
A Framework for Interactive Proof….Pages 161-175
Supporting User-Defined Notations When Integrating Scientific Text-Editors with Proof Assistance Systems….Pages 176-190
Mizar Course in Logic and Set Theory….Pages 191-204
Using Formal Concept Analysis in Mathematical Discovery….Pages 205-220
Cooperative Repositories for Formal Proofs….Pages 221-234
Revisions as an Essential Tool to Maintain Mathematical Repositories….Pages 235-249
The Layers of Logiweb….Pages 250-264
Formal Representation of Mathematics in a Dependently Typed Set Theory….Pages 265-279
Restoring Natural Language as a Computerised Mathematics Input Method….Pages 280-295
Narrative Structure of Mathematical Texts….Pages 296-312
Re examining the MKM Value Proposition: From Math Web Search to Math Web Re Search….Pages 313-326
Alternative Aggregates in Mizar ….Pages 327-341
An Approach to Mathematical Search Through Query Formulation and Data Normalization….Pages 342-355
Extended Formula Normalization for ε -Retrieval and Sharing of Mathematical Knowledge….Pages 356-370
Towards Mathematical Knowledge Management for Electrical Engineering….Pages 371-380
Spurious Disambiguation Error Detection….Pages 381-392
Methods of Relevance Ranking and Hit-content Generation in Math Search….Pages 393-406
Back Matter….Pages –