Documentation

Reasoning Library

The theory behind artificial reasoning, and the strategies that implement it as gated graph designs.

Designing how an AI reasons — the shape of the algorithm it thinks through, distinct from the model underneath and the prompts on top — turned out to need names we did not find waiting for us. The discipline we call cognitive engineering: treating the structure of reasoning as something you can specify, measure, and improve, the way you would any other engineered artifact.

The product of that discipline now has a name of its own: artificial reasoning — reasoning engineered as an explicit, inspectable computation rather than left to emerge inside a model. Cognitive engineering is the practice; artificial reasoning is what it builds.

The core Four reads, in order — the whole position

Theory Going deeper, ground up

Application From problem to artifact

Then see the artifact itself: the sample Regulator Dossier →

This library is a manual in two parts. Foundations lays out the theory — why output quality decomposes into factors and structure is the leverage point, how that structure decomposes into levels you can design, and how it is measured. The Graph Library catalogs the reasoning strategies as gated graph designs — each with a full walkthrough, its gates specified operationally, and worked use cases — authored in Reason, our graph-definition language, when deployed. New strategies are introduced family by family in the Reasoning Strategies series on the blog.

Section 1

Foundations

The theory, formally — why structure matters, how it decomposes, and how it is measured.

The R/K/G Framework

A mathematical framework for cognitive system output quality, extending the Cattell–Horn–Carroll tradition

R = reasoning capability · K = knowledge sufficiency · G = graph design quality

Why the Curve Has This Shape

Companion to R/K/G — an intuitive derivation of the equation from three assumptions, and why it is a candidate to be fit, not a law

diminishing returns → log · compounding → power law · gap-closing → linear amplification

Strategy, Tactics, and Implementation

The three levels of reasoning design — and the three-layer meta-strategy every effective strategy moves through

strategy = the shape of thought · tactics = the topology · implementation = the prompt set

Reasoning Circuit Complexity

A formal cost model and structural analysis of reasoning graphs, in the lineage of circuit complexity theory

D(G) = depth · W(G) = width · ν(G) = verification density · classes G₁–G₅

04

The Reason Language

A manual for the language IRG graphs are authored in, with worked examples — in alpha, publishing when the surface stabilizes

:gen · :crt · :rev · :arb · :ass · :gat · :act — nodes, gates, routes

Reference

Upcoming

Section 2

Graph Library

The reasoning strategies as gated graph designs — each with a full walkthrough, its gates specified operationally, and worked use cases.

Strategies grouped by the family they come from. Epistemic, Problem-Solving, Argumentative, and Scientific are published and expand to their graphs; the rest are named here and arrive one family at a time.

Epistemic The three canonical modes of inference

3 graphs

Abductive Reasoning

C. S. Peirce · inference to the best explanation

OBSERVE anomaly → GENERATE hypotheses ∥ → EVALUATE → SELECT · gates: surprise · plausibility

Diagnostics · root-cause

Deductive Reasoning

Aristotle · truth-preserving derivation

RETRIEVE premises → APPLY rules → VERIFY · gates: validity · soundness

Eligibility · compliance

Inductive Reasoning

Hume & Mill · generalization from instances

RETRIEVE instances ∥ → CLUSTER → EVALUATE confidence · gates: sufficiency · diversity

Trend · precedent

Problem-Solving From a known goal to a defensible path

5 graphs

Descartes & Pólya · split, solve, recompose

GENERATE parts → SOLVE each ∥ → EVALUATE recompose → ARBITER · gates: coverage · scope

Adjudication · KYC

Means-Ends Analysis

Newell & Simon · reduce the largest difference

EVALUATE gap → GENERATE operator → VERIFY shrink ↻ → ARBITER · gate: progress

Remediation · deadlines

Analogical Reasoning

Precedent tradition · structure over surface

RETRIEVE source → GENERATE mapping → CRITIQUE disanalogies → EVALUATE transfer · gate: mapping

Precedent · policy

Constraint Satisfaction

CSP tradition · every rule holds at once

GENERATE variables → RETRIEVE constraints → EVALUATE propagate → VERIFY all hold · gate: satisfaction

Structuring · eligibility

Working Backward

Pappus & Pólya · from the goal to the given

EVALUATE end state → GENERATE prerequisites ← → VERIFY chain touches today · gate: grounding

Statutory clocks · readiness

Argumentative Positions that must survive challenge

3 graphs

Toulmin Argumentation

Stephen Toulmin · claim, grounds, warrant, rebuttal

GENERATE claim → grounds → warrant → CRITIQUE rebuttal → ARBITER · gate: ruling

Coverage · disputes

Dialectical Reasoning

Dialectic tradition · thesis, antithesis, synthesis

GENERATE thesis ∥ antithesis → CRITIQUE tension → ARBITER synthesis · gate: answers both

Trade-offs · contested

Steelman / Charitable Interpretation

Charitable interpretation · engage the strongest version

GENERATE position ∥ strongest opposing → EVALUATE vs best → ARBITER · gate: ruling

Denials · risk review

Scientific Belief that has earned the right to move

2 graphs

Hypothetico-Deductive Method

Scientific method · predict, then try to break it

GENERATE hypothesis → DEDUCE predictions → RETRIEVE evidence → CRITIQUE disconfirm · gates: prediction · disconfirmation

Investigations · root cause

Bayesian Updating

Bayes & Laplace · belief in proportion to evidence

RETRIEVE prior → RETRIEVE evidence → EVALUATE diagnosticity → UPDATE ↻ · gates: prior · calibration

Monitoring · risk scoring

Design & Linguistic Double Diamond, Lateral Thinking, Schema Instantiation, Pragmatic Inference

Part 6 Upcoming

Domain-Specific IRAC, Differential Diagnosis, Red Team / Adversarial

Part 7 Upcoming

See the framework running live →