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Multi-dimensional
and multi-linear logic


Contents

Linear logic Multi-linear logic Multi-dimensional logic Multi-dimensional+ logic Summary of the different dimensionalities of logical systems



Linear logic behaves in means of exact determinism, and the binary nature of linear logic systems is essential.
However, this doesn't apply to multi-dimensional logic.

Then there is multi-linear logic, which behaves a bit like both linear as well as multi-dimensional logic.
The commonalisties and differencies will be summarized in a table in the following section.


Linear logic


Linear logic can be regarded as a one-dimensional stream of ideas.
Linear logical systems have merely fixed processes and fixed structures. These systems are more likely to be categorized as a level 1 complexity.
These systems can be illustrated as lines or linear streams without branching.


Multi-linear logic


Multi-linear logic can be regarded as a two-dimensional stream of ideas.
Multi-linear logical systems have merely fixed processes, but tend to offer flexible structures. These systems are more likely to be categorized as a level 2 complexity.
These systems can be illustrated as tree diagrams/ fractals where the flow of interaction lies only in front. The system doesn't rewrite its own processes and therefore the processes are fixed. Interference is only possible within its own system. Entropy and emergence ratio is 1:0.


Multi-dimensional logic


Multi-dimensional logic can be regarded as a two(+)/3-dimensional stream of ideas.
Multi-dimensional logical systems have flexible processes and flexible structures. These systems are more likely to be categorized as a level 3 complexity. These systems can be illustrated as tree diagrams/ fractal that can f-interfere and rewrite its own processes. The flow of interaction isn't only limited to the forward direction. Interference is only possible with itself.
Entropy and emergence ratio is equal, 1:1


Multi-dimensional+ logic


Multi-dimensional+ logic can be regarded as a 3-dimensional stream of ideas.
Multi-dimensional+ logical systems have flexible processes and flexible structures. These systems are more likely to be categorized as a level 3 complexity and above. These systems can be illustrated as tree diagrams/ fractal that can self-interfere and rewrite its own processes. The flow of interaction isn't only limited to the forward direction. Interference is possible both to itself as well as subset/superset systems/ "branches".
Entropy and emergence ratio is 1:2.


Summary of the different dimensionalities of logical systems


The direction of interaction has a relation to entropy;
An only forwards direction leads to increase of complexity without emergence (a process of self-simplification) and thus increases the entropy directly.
A backwards direction of interaction means an indirect decrease of complexity through an increase of complexity, which is the result of emergent behavior. The entropy degree partly gets an indirect factor of inversion.

A phenonmenon was recognized by s group of scientists some weeks ago, in which a special quantum system seems to "move backwards in time" as measured by a decrease of entropy.
This could be possible through the reaction emergent behavior creates; In this case emergence leads to an inversion of the entropy degree, in which a system gets so complex it simplifies itself. This leads to a decrease of relative complexity.


Type of logcial system Linear system multi-linear system multi-dimensional system multi-dimensio
-
nal+ system
Complexity level 1 2 3 ≥4
Dimensionality 1 2 3 >3
Represented by line tree diagram/ fractal tree diagram/ fractal tree-diagram/ fractal
Direction of interaction only forwards only forwards only forwards both forwards as well as backwards
Entropy - emergence ratio 0:0 1:0 1:1 1:2

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