Frame your imagination with these Visualization techniques:

Lets analyze whether we can build a conceptual language grammar and its language properties as operations with a geometry which references a concept of meta-model 🙂

Frame your imagination with these Visualization techniques:

Gallery

LMR

Metamodel

wikipedia metamodeling

Opinion to wiki metamodeling:

The relationship between Symbol and Concept can never be symmetric to the relationship between Symbol and Occurrence. The graphic has two undefined lines and does not reference itself as symbolic depiction of a model as its meta-model.

Towards metamodeling:

With any Ansatz to specify the model and make it more consistent with its self-reference capacity as a formalism, we center the symbol terminus and develop the context (environment) around it. As such, a Gestalt of the relationships between concepts will form. For simplicity we skip to a rudimentary meta model which references and calls the model and meta-model concepts explicit and as such will grow in dimensionality by a means of fractalization.

Developing a conceptual representation mechanism

                      M: Concept as 'super'-metric or hypersymbolic-quality

L: Descriptor as active element

                                                         R: Occurrence as passive element

Sketch for LMR-valence display of a meta-model theory for concept formalization

We left aside the notion of 'class' as this would require introduction of Hierarchy [another element which was neglected in the original wiki graphic]

Displaying multidimensional networks (multiplexa) in 2D or 3D is not trivial. The same is true for ternary multivalent logic and polyvalent logic. With its fractal systematic, LMR is the simplest polyvalent logic - and by any means the minimum tiling for conceptual languages.

LMR is a three-dimensional trimodal logic. Each of the three 'branches' = valences has three dimensions. The resulting logic map has 27 transition functions between the pivots (there are 9 pivots and the excluded origin nor surrounding topology is not discussed yet)

FMC Metamodel

The Equilibrium [Model] and Metamodel [metastability]

For trimodal logic to be at its resting state means the values of valence will put the ε into rest. In xd4, such a structure would disappear (which is forbidden) but in 3D-Logic it is the most useful first step towards gauge theory of hypercomplex systems. Equilibrium requires a distance measure, for which the delta-conversion is applied.

How to introduce internal metrics between the dimensions of a logics valence?

A metric is neglecting possible other measures and has an axiomatic 'coordinate' within a higher order metric

δ-conversion

Meta-Modeling [Concept equilibrium]

To model chaotic behavior and diversity, the Concept of oscillation and chaos-oscillators comes to mind. Small changes close to the origin of the phase induction will cause large deviations at the propagated measure dimension (i.e. its position within a metric or a specified or calculated value)

The Equilibrium [Model]

To model equilibrium we must assume a higher order metric is allowed and does not impact the valence itself

The Metamodel [Metastability]

To calculate stability means to induce a change of the surrounding (local) topology ('change reality') or an internal mechanism of the valence should prefer homeostasis (relaxation, eventually symmetry)

The complex Equilibrium [Model]

With different gradients between the valences, the resulting 2D map is not trivially 'visualizable' as each of the perspectives will render the geometry different. A geometric evolution from one form to another could be visualized in the way seen there:

Geometric Evolution to model valence-interactions and interference. As such, valences are curled tensors.

With introduction of geometric formalisms to logic, new kinds of correlates and valence can be specified. With LMR we explore one of the easiest models of geometry, the planar triangle.

<aside> 🔄 An example

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