Thomas Mahler, Essen
|Gotthard GŁnthers 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 (GŁnthers `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
Please download the complete
package as a ZIP-archive or pick
the uncompressed source code files:
|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.
|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.