PolyContexturality:
Conceptual Pattern that can be applied to formalize self-referential systems. It describes such
system as interacting Domains -- Contextures. It originates from studies in polycontextural logics.
Problem:
Implementation of self-referential systems. Formalization of self-referentiality with classical
concepts results either in reduction of actual complexity or logical contradictions i.e failing
computations.
Solution:
Resolve logical contradictions by describing the system as a distributed set of interacting subsystems. The interaction can be modelled with the Proemial Relationship, a coordinating parallel operation (P-Combinator). The operational semantics of this P-Combinator can be defined by a
VirtualMachine.
See
http://www.techno.net/pcl/tm/plisp/ENGLISH.EPS for a first step implementation of this Combinator.
Example:
Development of a self-correcting OCR Software:
To identify a single letter, the software does not only need knowledge of single letters but also of syntax, grammar and semantics of a given language. Traditional solutions would use a bottom-up or a top-down approach. A polycontextural architecture would formalize this situation as a
simultaneous interaction of 4 domains (Lexical, syntactical, grammatical, semantical contexture).
Related Patterns:
Reflection (see
OnReflection) and
MetaLevel Architectures (see also
MetaObjectProtocol,
OpenImplementation,
PoSa)
Known Uses:
Self-referential, Reflective and introspective Systems have been modelled using Polycontexturality.
See official Polycontexturality Site at:
http://www.techno.net/pcl
--
ThomasMahler
Does it have any relationship with category theory or non-well-founded set theory? --
MichaelFeathers
Yes. There is a research group for computational category theory at the RISC Institute, Linz, Austria (
http://www.risc.uni-linz.ac.at/research/category/risc/ ) which has been working on this subject.
They published a paper on cooperative agents which relates Polycontexturality to sheaf and fiber bundle theory (
ftp://ftp.mpi-sb.mpg.de/pub/igpl/Journal/V4-3/index.html#Pfalzgraf).
--
ThomasMahler