Poly Contexturality

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