Morphogrammatik

Eine Einführung in die
Theorie der Logischen Form

Thomas Mahler, Essen
E-Mail: tm@bov.de
WWW: http://www.techno.net/pkl

Abstract

Gotthard Günthers works on polycontextural logics emphasized the importance of morphogrammatics as a general pre-logical theory of the architecture of logic-systems. In spite of their theoretical significance morphogrammatics have not yet been explicated as a formal theory.
The present work locates morphogrammatics in the intersection of kenogrammatics and polycontextural logic and explains it against the background of these theories. In part I Kenogrammatics are formally introduced as an underlying general theory of semiotic processes. In part II Kenogrammatic concepts, structures and operations are used to develop the mathematical theory of morphogrammatics. Part III classifies and analyses combinatorical properties of morphogrammatic structures and operations. Part IV is dedicated to applications of morphogrammatics to logic and computer science: It gives an outline of the formal foundation of logical systems (Günthers `place-value logic' and polycontextural logic) by morphogrammatics (chapter 9). In chapter 10 an implementation of the `proemial-relation' is designed, which is suggested as an extension of functional programming and as an implementation-technique for computational reflection and process communication.

Keywords: artificial intelligence, antinomies, autopoieses, circular systems, combinatory logics computational reflection, cybernetics, formal languages, foundations of mathematics, functional programming, kenogrammatics, logic, morphogrammatics, number theory, parallel processing, polycontextural logic, proemiality, process communication, selfreferential systems, semiotics, simultaneity.

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Please download the complete book in DVI form (250 pages, 990 Kb): MG-Buch. Due to the intensive use of mathematical formulars and vectorgraphics we provide this work only as a ready to view DVI-file. You will need a TEX-Implementation (like emtex, ftp://ftp.dante.de) to view this document. Sorry for this, but I prefer to do creative work rather than converting files all night long.

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 (an NT-implentation is on the way). 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

MorphoLab 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 with the ultimate PCL-Toolkit. Until now it does not include an implementation of the Proemial Relationship.

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

Enjoy!