Peter Schodl

Department of Mathematics
University of Vienna
Nordbergstraße 15,
1090 Vienna, Austria
Room C.518
email: peter.schodl (at) univie.ac.at

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Welcome!
This is my homepage, containing information about my work at the University of Vienna.

The FMathL Project

The FMathL Project started May 2008, financed by the FWF with the goal to create a software to ease human-computer communication of mathematical content. Roughly speaking, we want to teach a computer to understand a LaTeX-file well enough to communicate its essential content to other software. Firstly, we concentrate on mathematical text specifying optimization problems.

In July 2009, I gave a talk at the MKM09 about the current status of the FMathL project. The slides of this talk can be found here.

In February 2010, I gave a talk at the Seminar Formale Mathematik of the Naproche project about the implementation of MoSMath, which is a part of the FMathL project. The slides of this talk can be found here.

In October 2010, I presented a poster at the International Conference on Knowledge Engineering and Ontology Development (KEOD) about the vision behind the FMathL project.

The corresponding position paper has been published as:
Neumaier A. and Schodl P.
A FRAMEWORK FOR REPRESENTING AND PROCESSING ARBITRARY MATHEMATICS [PDF of a preprint]
In: Proceedings of the International Conference on Knowledge Engineering and Ontology Development (2010), pages 476-479

In August 2011, I introduced the type system of FMathL at the LSFA 11. The slides of this talk can be found here.

The FMathL Project
The MoSMath Project
Arnold Neumaier's Homepage
Hermann Schichl's Homepage


For some interesting related research, visit:

Attempto project, interface from a controlled natural language to a variant of first order logic.
MathLang, a language for computerizing mathematical text.
MathNat, a project for developing tools to enable automatic formalization of mathematical text.
Naproche , an interface from a controlled natural language to proof checking software.
SAD system, automated processing of mathematical texts written in a special language.
The Grammatical Framework, programming language for multilingual grammar applications.
Z and CADiZ, a language for formal specification of software, also applicable for mathematics.


PhD thesis

As a part of the FMathL-Project, I have written my PhD thesis, titeled "Foundations for a Self-Reflective, Context-Aware Semantic Representation of Mathematical Specifications" [PDF].

Work in progress:
Arnold Neumaier, Peter Schodl
"A Semantic virtual Machine" [PDF]
Work in progress:
Peter Schodl, Arnold Neumaier
"The FMathL type system" [PDF]
Work in progress:
Arnold Neumaier, Peter Schodl
"An experimental grammar for German mathematical text" [PDF]

All comments are welcome!


Multivalued mappings

In 2005, I wrote my diploma thesis about continuity of multivalued mappings (also called set-valued mappings), supervised by Arnold Neumaier.

Starting point was a gap in a proof in the book 'Interval methods for Systems of Equations' by Prof. Neumaier.

Other important inputs came from Alexandre Goldsztejn and Stefan Ratschan.

For an overview and a large bibliography of this field, I found the book 'Topological Fixed Point Theory of Multivalued Mappings' by Lech Gornievicz (1999) most helpful.

Accepted for publication in "Reliable Computing":
Peter Schodl, Arnold Neumaier
"Continuity notions for multi-valued mappings with possibly disconnected images" [PDF]

Other useful or interesting links

Csound, a programming language and compiler for sound rendering.
KNOPPIX/Math, a Linux Live-CD with a focus on mathematical software.
Librivox, a site for free audio books from the public domain.
LOUT, a LaTeX-like typesetting system smaller than 2MB.
NaNoWriMo, the national novel writing month.