# Ontology · Reasoning

> Every algorithm grammar is an instance of the derivation loop, which has ten stages, each on one reasoning axis, joined by transitions that sequence, gate or…

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## Entries

- [The derivation loop](https://banes-lab.com/ontology/reasoning/reason-loop-derivation-loop.md): Every algorithm grammar is an instance of the derivation loop, which has ten stages, each on one reasoning axis, joined by transitions that sequence, gate or…
- [The substrate](https://banes-lab.com/ontology/reasoning/the-substrate.md): Beneath the loop lies the generative substrate, meaning the cycle every node passes through, the recursion that turns emergence back into a new difference, and…
- [The reasoning layers](https://banes-lab.com/ontology/reasoning/the-reasoning-layers.md): The reasoning axes are arranged on these layers, each listed with the question it answers and the axes it holds.
- [The axes](https://banes-lab.com/ontology/reasoning/the-axes.md): Each reasoning axis is a typed, terminating question on one layer, listed with the nodes a run may select on it and the contracts positioned on it.
- [The nodes](https://banes-lab.com/ontology/reasoning/the-nodes.md): Every node on the axes is listed with the concept it resolves to, the question it asks, the math type it yields, the shape of its answer, its decision test and…
- [The mathematics](https://banes-lab.com/ontology/reasoning/the-mathematics.md): The predicates are typed by these math types, each listed with its contracts and the domains of mathematics it draws on.
- [The dimensions](https://banes-lab.com/ontology/reasoning/the-dimensions.md): The ontological dimensions are what can be observed about a subject, and each is listed with the test surfaces that observe it.
- [The lenses](https://banes-lab.com/ontology/reasoning/the-lenses.md): The analysis lenses are how a subject is seen.
- [The modes](https://banes-lab.com/ontology/reasoning/the-modes.md): Each reasoning mode is listed with the practice it names and the techniques that work in it.
- [The representations](https://banes-lab.com/ontology/reasoning/the-representations.md): A result can be encoded in any of these representation layers.
- [The pattern types](https://banes-lab.com/ontology/reasoning/the-pattern-types.md): Each pattern type is listed with the mathematical viewpoint it takes.
- [The models](https://banes-lab.com/ontology/reasoning/the-models.md): The models are sequences that restate the same cycle from different starting points.
- [The universal axes](https://banes-lab.com/ontology/reasoning/the-universal-axes.md): The five universal axes are listed with the dimensions each one subsumes and the lenses that sit on it.
- [The test surfaces](https://banes-lab.com/ontology/reasoning/the-test-surfaces.md): The test surfaces are what a system can be wrong about.
- [The techniques](https://banes-lab.com/ontology/reasoning/the-techniques.md): Each technique a surface is observed by works in one reasoning mode and is listed with the surfaces that use it.
- [The invariants](https://banes-lab.com/ontology/reasoning/the-invariants.md): Each invariant the test surfaces assert is listed with the surfaces that assert it.
- [The uncovered cells](https://banes-lab.com/ontology/reasoning/the-uncovered-cells.md): These cells of the dimension and lens grid are not yet covered by any surface. The list is derived from the grid and the surfaces, never stored.
- [The maps](https://banes-lab.com/ontology/reasoning/the-maps.md): 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 groundings](https://banes-lab.com/ontology/reasoning/the-groundings.md): Every grounding edge the reasoning face declares is listed with the record it leaves from and the record or grammar it lands on, or with the label it carries…