morphoGrammatics

An Introduction to the
Theory of Logical Form


Thomas Mahler, Essen
E-Mail: [email protected]
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.

 
     
  Download the complete text  
  Please download the complete book (293 pages) in DVI form (990 Kb) or in EPS form (1,4 MB).  
     
  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 provided by Bell Laboratories, which is currently availabe for UNIX and Win95/NT Machines.

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, which you will find in the next section.

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

Enjoy!

  
     
  Implementation of the Proemial Relationship (PRS)  
  The implementation of PRS by means of a virtual graphreduction machine as described in the above book has been ported to JAVA. Therefore we can now present a web-enabled version of this implementation.
Visit our new pLISP Homepage for experimenting with this unique VM.