Hilbert II |
Formal Correct Mathematical Knowledge |
|
Overview | quick start and feature summary |
Project Goals | about this project |
Release Contents | detailed directory description of this release |
Further Installation | some more or less optional adjustments |
Licenses | these licenses apply |
Future Development | short range project plan |
This is an unstable development release of Hilbert II. In the tradition of Hilbert's program the project creates a formal correct (checkable by a proof verifier) but readable (like an ordinary LaTeX textbook) mathematical knowledge base which is freely accessible within the internet. The project starts with logic and set theory.
This release contains a specification of XML files that can have mathematical content. It can also produce LaTeX files out of QEDEQ XML files, samples and a script with the beginning of axiomatic set theory are included.
You could read the change history to know the difference to the previous release.
Precondition is a Java Runtime Environment, at least version 1.4. From Download Java 2 Platform you could get the Java Runtime Environment J2SE v 1.4.2 JRE.
To start the application call:
org.qedeq.rel.test.text.Xml2Latex <xmlFile>
or for an interactive swing window:
org.qedeq.rel.test.gui.Xml2Other
The classpath must include the files in the lib directory.
You can also simply start the textual or GUI version by starting the batch scripts in directory bin.
Sample XML files can be found in the sample directory. The main structure of an QEDEQ XML file looks like the LaTeX book format. There is a special kind of subsections called node
that contain an abbreviation, axiom, definition or proposition. Each node is labeled and could be referenced by that label. Here is the XSD and here it's documentation. The root element is called QEDEQ.
This release includes the source code and the JUnit test classes. The code coverage results of these tests where produced by .
The goal of Hilbert II is decentralised access to verified and readable mathematical knowledge. The knowledge base contains mathematical texts in different languages and detail levels, axioms, definitions, propositions and their proofs. Beside common non formal proofs the system includes formal proofs that were verified by a proof checker.
The mathematical axioms, definitions and propositions are combined to so-called QEDEQ modules. Such a module could be seen as a mathematical textbook. At least all proposition formulas are written in a formal language and each proposition can also have a formal correct proof. The proposition is verified iff it has a formal proof and all required propositions are also verified.
Hilbert II will provide a program suite that enables a mathematician to put data into that knowledge base and retrieve various documents and analyze results out of the system. This includes the generation of LaTeX files that look like a common mathematical textbook and the answer to questions like "assumes this theorem the axiom of choice?" for verified propositions. As it's name already suggests, this project is in the tradition of Hilbert's program.
Because this system is not centrally administrated and references to any location in the internet are possible, a world wide mathematical knowledge base could be build. Any proof of a theorem in this "mathematical web" could be drilled down to the very elementary rules and axioms. Think of an incredible number of mathematical textbooks with hyperlinks and each of its proofs could be verified by Hilbert II. For each theorem the dependency of other theorems, definitions and axioms could be easily derived.
See also under QEDEQ basic concept for more project details. This document was generated out of the following XML file: qedeq_basic_concept.xml.
This release contains also the beginning of a script about axiomatic set theory. This script is also available in German and has this XML source.
The XML files have a formal structure that is defined here or here. The logical language is described in qedeq_logic_language_en.pdf (in development).
Directory | Description |
---|---|
bin |
executable files |
xml2othergui.bat |
batch file to start the application with GUI |
xml2othergui.sh |
unix script to start the application with GUI |
xml2latex.bat |
batch file to start the application in text mode |
xml2latex.sh |
unix script to start the application in text mode |
config |
configuration files |
log4j.properties |
log4j property file, change "FATAL" to "DEBUG" to get a log file |
doc |
documentation |
project |
project specific |
qedeq_basic_concept_en.pdf |
basic concept of Hilbert II |
qedeq_logic_language_en.pdf |
explanation of the logical language of Hilbert II (in development) |
projektbeschreibung.pdf |
project description (in German, a little bit outdated) |
changes.txt |
change history to previous versions |
clover |
code coverage results of JUnit tests by |
math |
mathematical texts |
qedeq_set_theory_v1_en.pdf |
beginning of axiomatic set theory, this is already a QEDEQ module |
qedeq_sample1_en.pdf |
mathematical sample: small QEDEQ module |
axiomatic_set_theory.txt |
beginning of set theory as non formal (ascii text) file, it shows the intention of this project (parts in German) |
qedeq_logic_v1_en.pdf |
logical background (in German) |
javadoc |
java documentation of Hilbert II |
lib |
libraries |
commons-logging-1.1.jar |
apache commons logging component |
log4j-1.2.14.jar |
log4j logging implementation |
qedeq_se.jar |
binary release of Hilbert II |
xercesImpl.jar |
apache XML parser xerces |
xml-apis.jar |
XML standard API definition |
license |
license files |
license/apache_license.txt |
apache software license |
license/fdl.html |
GNU Free Documentation License |
license/gpl.html |
GNU General Public License |
log |
log files are written herein |
sample |
sample XML files |
qedeq_basic_concept.xml |
qedeq basic concept as qedeq XML document |
qedeq_set_theory_v1.xml |
beginning of axiomatic set theory |
qedeq_sample1.xml |
mathematical sample module |
qedeq_sample2_error.xml |
semantic error in QEDEQ file |
qedeq_sample3_error.xml |
syntax error in XML file, violates XML syntax |
qedeq_sample4_error.xml |
syntax error in XML file, violates XSD |
qedeq_sample5_error.xml |
logic error in XML file, quantify over already bound subject variable |
qedeq_sample6_error.xml |
logic error in XML file, "ins" is an unknown predicate |
src |
source code of Hilbert II |
srcTest |
source code of JUnit tests |
xml |
XML schemata and their documentation |
qedeq.xsd |
XSD for QEDEQ format |
qedeq.html |
documentation of QEDEQ XSD |
parser.xsd |
XSD for operator definition for text parser |
parser.html |
documentation of parser XSD |
qedeq |
|
index.html |
another documentation of QEDEQ XSD |
Beside the steps mentioned in Overview you should install a correction for the buggy LaTeX package longtable. One possiblity is this patch from Chung-chieh Shan. It was used to produce the provided PDF files.
The QEDEQ XML files stand under the GNU Free Documentation License (GFDL), the software of this project under the GNU General Public License (GPL). For XML parsing the apache parser is used which falls under the apache license.
For the current source code you could browse the subversion or cvs tree.
Here are descriptions of the next minor releases. Subversions are not listed. All these releases are characterised as "unstable" and are only of interest for developers.
0.01 brigand |
First XSD releases. XML could be parsed and value objects are created. Very simple generation of LaTeX files is possible. There are two QEDEQ modules: the project handbook and a mathematical example. Beside the XSD verification no checking is done. The latex generation works directly on the value objects. |
0.02 moster |
Some elements of the BO (business object) layer exist. The script of axomatic set theory includes at least most of the axioms. First attempts of a small LaTeX to QEDEQ XML converter. |
0.03 mongaga |
Formal checks for single formulas could be done ("is this formula well formed"). |
0.04 toffle |
Formal proofs can be written down. |