''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