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PolyContextural Computing Lab
© '98/2004 PCL Group
Design & Realisation:
Th. Mahler







As a result of the efforts in formalisation and implementation of PCL we can now present a collection of experimental software tools for the transclassical calculi of PCL, Kenogrammatics and Morphogrammatics.

Polycontextural Logics

Downloadable Software-Lab for PCL

In one of our research projects we developed a Software Lab for PCL, including an automatic proof-generator for PCL.
For running this code you will need Standard ML (including modules and functors) like The New Jersey SML, which is currently availabe only for UNIX-machines (an NT-implentation is on the way).

Sorry, the code is not yet out from Beta-Testing!


Downloadable Software-Lab for Morphogrammatics

For those who want to 'see' Kenogrammatics, Morphogrammatics, the transclassical proemial relationship etc. working on a classical Turing machine (i.e. your personal computer) we provide the SML source code as documented in the above mentioned textbook. For running this code you will need Standard ML (including functors) like The New Jersey SML, which is currently availabe only for UNIX-machines and WinNT. For the DOS or Windows user a tiny ML version called Moscow ML is available, which does not support functors. But everything else *should* work.

Please download the complete package as a ZIP-archive or pick the uncompressed source code files:
Kenogrammatics and Morphogrammatics
Basic Parser
Lambda-Term-reader (This parser is implemented with functors, so you can't use it with Moscow ML.)
The Lambda to Combinatory Logic compiler
The Multitasking graph-reduction engine
The start screen
The Make-file

JAVA Implementation of the Proemial Combinator-machine

JAVA-LISP is an experimental Implementation of reflective functional Programming. It contains a very simple Lexer and Parser for a lambda-calculus language in lisp-syntax. The Lambda terms are compiled to variablefree Combinator Graphs.
The virtual Graph-Reduction-Machine that reduces the Combinator-graph distinguishes between strict and non-strict operations. Strict operations have to be evaluated even if we obey lazy evaluation and can therefor be evaluated in parallel to the main Computation.
The parallel computations are added to a global task pool, which is maintained by a stochastic scheduler.

In addition to this basic implemenation a special Combinator P is introduced which performs an asyncronous parallelism of two given applications.
P (app1 rator1) (app2 rator2) -->
(P parEval(app1 rator1) parEval(app2 rator2))

If rator1 and app2 point to the same object X, you get the funny result, that the same object is used simultaneously as Operand (by app1) and as Operator (for rator2), because both applications are evaluated in parallel:
P (app1 X) (X rator2)

This special situation is quite ambigious and "dangerous" for it disturbs the predictability of computational systems.
Although it looks a bit awkward and arises many problems in traditional calculi, this Relationship can be formalized by PolyContextural Logics (PCL), which describes it as the "Proemial relationship"

This Relationship is useful in formalizing self-referential, contradictory, autopoietic etc. systems. It is also quite helpful in the formalisation of meta-level architectures and computational reflection.

The aim of the JAVA-LISP project is to build a LISP-like Programming language which is capable of implementing such architecture.

As you will recognise, the implementation is rather small and includes until now only the most necessary features.
Especially the performance has to be enhanced (an optimizing compiler is on the way..)
However you can feel free to experiment with this toolbox, improve it, discard it... or give some feedback for further developments.

MorphoLab 1.0 for Win95/WinNT out now!

According to the many requests of the general public and our industry-partners we proudly present a Win95/WinNT Version of the MorphoLab. This Program enhances your Windows System with the ultimate PCL-Software. Until now it does not include an implementation of the Proemial Relationship.

Get your Copy now! (200K, Executable only, requires vbrun400.dll etc.)
Complete Installation Package (1,56 MB)


Rudolf Kaehr: Das graphematische Problem einer Formalisierung der transklassischen Logik Gotthard GŁnthers, 1981
This text is a paper which goes back to the 70th and was in some sort a first attempt to formalize polycontextural logics in the game of disseminated Smullyan Frameworks with the use/abuse of Category theory. It is a predessor design to the attempts of formalizing and implementing PCL in the framework of ML, as published in the early 90th. See below.

Catharina Kennedy: Logical Problems of Cognitive Modelling (1995)
Second-Order Cybernetics.Introduction to the logical problems of self-referential systems and some motivations to their modelling in polycontextural logics. (internal use only).

Get the description of the first implementation of a semi-automatic Tableaux-Prover for polycontextural logics developed between 1988/1993 in ML by Steven Bashford and Johannes 5 Joemann (german).
Polykontexturale Logik. Tableaux-Beweiser. DOCUMENTATION.

Polykontexturale Logik. Tableaux-Beweiser. Sources of ML-IMPLEMENTATION.

    © '98/2004 PCL-Group