# The maps

> The reasoning face carries these maps beside its records, namely the foundation sequence with the math types on each of its layers, the invariant groups, and…

Page: Ontology · Reasoning
Canonical: https://banes-lab.com/ontology/reasoning#the-maps

The reasoning face carries these maps beside its records, namely the foundation sequence with the math types on each of its layers, the invariant groups, and the operations a pattern admits.

### Foundation sequence

Details

logic-set-theory-axioms → [structure](https://banes-lab.com/records/reason/substrate-node-structure.md) → [change](https://banes-lab.com/records/reason/dimension-change.md) → relationships → possibility → application

### structure

Details

[algebra](https://banes-lab.com/records/reason/math-type-algebra.md), [geometry](https://banes-lab.com/records/reason/math-domain-geometry.md)

### change

Details

[analysis](https://banes-lab.com/records/reason/math-type-analysis.md), [dynamics](https://banes-lab.com/records/reason/universal-axis-dynamics.md)

### relationships

Details

[category-theory](https://banes-lab.com/records/reason/math-domain-category-theory.md), [information-theory](https://banes-lab.com/records/reason/math-type-information-theory.md)

### possibility

Details

[probability](https://banes-lab.com/records/reason/math-type-probability.md), [computation](https://banes-lab.com/records/reason/math-type-computation.md), [complexity](https://banes-lab.com/records/reason/lens-complexity.md)

### generative

Details

objects, relations, transformations, constraints, [emergence](https://banes-lab.com/records/reason/substrate-node-emergence.md)

### systemic

Details

entity, [relation](https://banes-lab.com/records/reason/substrate-node-relation.md), [state](https://banes-lab.com/records/reason/dimension-state.md), [transformation](https://banes-lab.com/records/reason/substrate-node-transformation.md), [constraint](https://banes-lab.com/records/reason/substrate-node-constraint.md), [information](https://banes-lab.com/records/reason/substrate-node-information.md), feedback, [emergence](https://banes-lab.com/records/reason/substrate-node-emergence.md)

### Members

Details

detection, [classification](https://banes-lab.com/records/reason/mode-classification.md), [explanation](https://banes-lab.com/records/reason/mode-explanation.md), [prediction](https://banes-lab.com/records/reason/mode-prediction.md), generation

## Links to

- [Structure](https://banes-lab.com/records/reason/substrate-node-structure.md)
- [Change](https://banes-lab.com/records/reason/dimension-change.md)
- [Algebra](https://banes-lab.com/records/reason/math-type-algebra.md)
- [Geometry](https://banes-lab.com/records/reason/math-domain-geometry.md)
- [Analysis](https://banes-lab.com/records/reason/math-type-analysis.md)
- [Dynamics](https://banes-lab.com/records/reason/universal-axis-dynamics.md)
- [Category Theory](https://banes-lab.com/records/reason/math-domain-category-theory.md)
- [Information Theory](https://banes-lab.com/records/reason/math-type-information-theory.md)
- [Probability](https://banes-lab.com/records/reason/math-type-probability.md)
- [Computation](https://banes-lab.com/records/reason/math-type-computation.md)
- [Complexity](https://banes-lab.com/records/reason/lens-complexity.md)
- [Emergence](https://banes-lab.com/records/reason/substrate-node-emergence.md)
- [Relation](https://banes-lab.com/records/reason/substrate-node-relation.md)
- [State](https://banes-lab.com/records/reason/dimension-state.md)
- [Transformation](https://banes-lab.com/records/reason/substrate-node-transformation.md)
- [Constraint](https://banes-lab.com/records/reason/substrate-node-constraint.md)
- [Information](https://banes-lab.com/records/reason/substrate-node-information.md)
- [Classification](https://banes-lab.com/records/reason/mode-classification.md)
- [Explanation](https://banes-lab.com/records/reason/mode-explanation.md)
- [Prediction](https://banes-lab.com/records/reason/mode-prediction.md)