From Metapattern to Ontoprise

1 Parallelism in Polycontextural Logic

Additionally to the well known OR- and AND-parallelism, polylogical systems offer two main extensions to the logical modeling and implementation of parallelism. First the distribution of the classical situation over several contextures and second, the trans-contextural distributions ruled by the different transjunctional operators. The distribution over several contextures corresponds to a concurrent parallelism where the different processes are independent but structured by the grid of distribution. The trans-contextural parallelism corresponds to a parallelism with logical interactions between different contextures.

"The tree corresponding to the search for a solution to a question seems open to various kinds of parallelism. The most obvious technique, called OR parallelism, allows processes to search disjunctive subtrees in parallel, reporting back to the parent node the result(s) of the search.
The advantage of OR parallelism is that the searches are completely independent of each other and may execute concurrently (except that both may share access to a common data base storing facts and rules). The process performing the search of one subtree does not communicate with processes searching other subtrees." Michael J. Quinn, 212, 1987

Prolog is based not only on its logic, used as an inference machine, but also on its semantics or ontology, realized as a data base. Therefore the process of parallelising has to deal with a deconstructive dis-weaving of the data base´s ontology.

1.1 Strategies towards a polycontextural parallelism in Prolog

Like in the case above, where the number systems had to be cloned, in the Prolog case, the data base has to be decomposed into disjunct parts. These separated conceptual parts, or conceptual subsystems, have to be distributed over different contextures in a mediated polycontexturality.

Additionally the Prolog parallelism which is based on OR- and AND-parallelism has to be mapped into distributed logics, that is, into a polylogical system.

The Prolog example allows to explain in more a plausible way the decomposition or cloning of the common universe of discourse, that is, the data base of facts, into different subsystems. And secondly it is easier to introduce parallelism based on polycontextural logic than on arithmetics and combinatory logics.

Polycontextural logic is not widely known but more accessible than combinatory poly-logic and poly-arithmetics, which I am just introducing. Additionally there exists since 1992 a working implementation of a tablex proof system of an interesting subsystem of polycontectural logics in ML, running on Unix systems like NeXT.

1.1.1 An intermediate step with Metapattern

As an intermediate step in the shift of conceptualization from a hierarchical to a heterarchical way of concept building it maybe helpful to use the strategy of metapattern (Wisse). Metapatterns are used as an new modeling strategy for complex informational systems. Metapatterns are not involved in changing the basic assumptions of programming languages or even their logic as with the PCL approach.

Metapatterns could be helpful to move the process of parallelisation from the OR- and AND-level, that is, from the logical level to the deeper level of the data base, with its facts and rules, shared by the classical parallelism.

She can relax on a fixed object orientation because - the metapattern determines that -situation and object are relative concepts (Wisse 2001). A particular situation is also object in another, higher-level situation. Likewise, an object can act as situation in which another, lower-level object resides. Situation, then, is a recursive function of object and relationship. Wisse

Hierarchy or chiasm?

It is this concept of situation that characteristically sets the metapattern apart from traditional object orientation (and provides it with advantages over OO; Wisse 2001). Compared to an object that (only) exists absolutely, an object believed to exist in a multitude a different situations can unambiguously be modeled - to be equiped - with corresponding behavioral multiplicity. Wisse 2001

The radical conclusion from the orientation at situational behavior is that an object's identification is behaviorally meaningless. The modeler does not have to explicitly include something like an original signature in all her models. Essentially a privileged situation may implied. It serves the only purpose of guaranteeing sameness or, its equivalent, persistent identity across (other) situations. Being a situation in its own right, when included in a model it is represented by a seperate context. Made explicit or not, its role is to authenticate an object's identity in other situations by establishing the signature in other contexts.

Identity as a network of nodes
Traditional object orientation assigns identity at the level of overall objects. Context orientation replaces this view of singular objects with that of plusrality within the object; the object always nneds a context to uniquely identify the relevant part of an overall object, which is what identifying nodes regulate. When behaviors are identical, no distinction between contexts is necessary.

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