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Locality, positionality and mobility in semiotic, categorical, diamond and kenomic systems.
Kenomic mobility compared with Agha’s Universal Actor System (UAM) and Middleware approach and Milner’s Bigraphs.
Sketch of an Architectonics of Kenomic Mobility.
Introducing trans- and diamond-Actors and their chiastic interplay as interactional and reflectional actors in knowledge grids.
3.1 Architectonics of kenomic Actor systems
1. Primitive actors are zero-order actors, they are not allowed to interact but are responsible for the whole actor system to work properly, i.e. without paradoxes and circularity.
Primitive actors are not active on the stage or arena but at the back-stage. Primitive actors are hidden actors.
Primitive actors are enabling the interactional actions of basic actors. Without the support by primitive actors self-destructive actions of infinite regress, antinomic cricularities (paradoxes) are unavoidable in classical, i.e. monocontextural actor systems.
Primitive actors are typical for monocontextural (formal) systems.
2. Basic actors are first-order actors, their definition is to interact with other actors of an actor system.
Basic actors are the actors on stage. They are playing the big interactional drama on a single arena.
Basic actors are playing on stage on the base of the hidden support by primitive actors.
Basic actors are playing on stage on the prospect of the open guidelines by meta-actors.
3. Meta-actors are second-order actors, they are responsible for the interactivity between different actor systems in a global actor system, like the WWC (World Wide Computing).
Meta-actors are the directors of the actor play. They manage the interactions between the actors, the actor systems and their universal distribution in a global interactional game. Hence, on a higher level they are also the organizational committee of the distributed actor systems.
This reflectional capacity of the meta-levels of second order systems can be iterated to meta-levels of the second-order system. That is, in the second-order systems, meta-reflections (introspection) can be iterated without changing the second-order status of the system. No meta-reflection leads to a third-order system. No iteration of meta-reflection has to collapse into first-order systems.
Meta-Actor systems, which are not yet embedded into the Diamond Actor system are not immun against the infinite regress problem imposed by the infinite iterability of meta-reflections.
Deepness of meta-reflections of second-order systems vs. broadness of object-reflection of first-order systems. This defines the reflectional Actor system for uni-versal interactions as it is exposed by Agha’s middleware approach.
4. Trans-actors are third-order actors, they are disseminating second-order actor systems over the kenomic matrix of polycontextural interactions. Polycontextural interactivity is pluri-versal.
trans -actors in polycontextural systems are represented by the so-called super-operators (identity, permutation, reduction, replication, bifurcation) defining operationally the interactionality between disseminated universal actor systems.
trans-actors are the mediators between disseminated actor systems. Mediators are the organizers of the interplay of different primordial actor systems.
Interactivity between disseminated actor systems is ruled by the mechanism of chiasms.
Chiasms are combining order-, exchange- and coincidence-relations between actors and actands on different levels of polycontexturality.
As a consequence of the chiastic structure of disseminated actor systems the primitivity of the primitive actors is resolved into a contextural relativity. What functions as a primitive in one contexture functions as a non-primitive in a neighbor contexture, and vice versa.
Hence, problems of circularity are restored at the situation of any single elementary contexture and resolved by the distribution of the construction of chiastic circularity over different contextures.
5. Diamond-actors are forth-order actors, they are embedding the activities of the trans-actors into diamonds.
Diamond-actors are enabling complex disseminated actor systems to incorporate the possibility of the new as the otherness of the actor system.
Diamond actors are playing a double role. They are responsible for the mobility system and are enabling its environment. The environment of a mobility system is the place of the otherness. This can incorporate attacking events and/or the surprise of the new.
Diamond actor systems are localized and positioned into the kenomic matrix.
The kenomic matrix is opening up spaces to general actor systems to place interactional, reflectional and interventional activities.