Reasoning Strategies, Part 1: The Epistemic Family

Why strategies, not just graphs

A practitioner sitting down to design a reasoning graph faces an immediate question: what shape should the reasoning take? Topology patterns — linear, diamond, tree, lattice, recursive, ensemble — describe structural possibilities. But they describe geometry, not intent. A diamond topology is a convergent shape; it does not tell you why you are converging, or what kind of reasoning produces that convergence. The same diamond can serve dialectical reasoning (thesis and antithesis resolving into synthesis), differential diagnosis (candidates narrowing to a diagnosis), or Bayesian updating (evidence streams converging on a posterior). Same geometry, three entirely different kinds of thought.

The distinction that resolves this is three levels of reasoning design, each independently variable and each with its own optimization target. Strategy is the reasoning shape — the abstract pattern of how thought proceeds. Tactics are the specific graph topology that instantiates the strategy. Implementation is the prompt set that drives execution at each node. A regulatory compliance task might take Toulmin argumentation as its strategy, a hub-and-spoke graph as its tactic, and precision-tuned prompts as its implementation — and you can swap any level without touching the others. The strategy determines which gates fire, what convergence means, and how quality is measured.

One more lens before the catalog. Every effective strategy, whatever discipline it comes from, moves through three layers of cognitive work: problem semantics (what the task actually is, and what “solved” means), representation transforms (restructuring the problem into a tractable form), and solver affordances (what the execution nodes can actually do). A well-designed graph touches all three explicitly. A poorly designed one jumps from problem semantics straight to solving — the cognitive equivalent of answering a question before understanding it. IRG’s gate system enforces the transitions: a gate between the representation transform and the solver checks that the problem has been reframed into a form the solver can accept.

This series walks the inventory a family at a time, in the format an engineer designing a graph actually needs: what the strategy is, what its graph looks like, which node classes and gates it requires, and when to reach for it. We start with the oldest family in the catalog: the three canonical modes of inference.

Abductive reasoning — inference to the best explanation

Abduction, formalized by Peirce, starts from a surprising fact and works toward the hypothesis that best explains it. It is the reasoning of the diagnostician and the incident responder: something anomalous happened; what account of the world makes it unsurprising?

The graph shape is a fan-out from the observation into parallel hypothesis generators, converging back through an evaluation gate. The phase sequence runs observation, hypothesis generation, evaluation, selection — mapped to Observe, Generate (in parallel, one per candidate explanation), Evaluate, Rank, and Select nodes. Two gates give the strategy its discipline. The surprise gate fires first: is the observation actually anomalous, or is the system about to explain something that needs no explanation? The plausibility gate fires per hypothesis: does this candidate genuinely account for the observation, or merely fail to contradict it?

Deploy abduction for diagnostics, root cause analysis, medical differentials, and anomaly investigation — anywhere the input is an effect and the output is the most defensible cause. Its characteristic failure, ungoverned, is premature convergence on the first plausible story; the parallel fan-out and the plausibility gate exist precisely to force the alternatives into existence before selection happens.

Deep dive: how the abductive graph works, step by step, with three grounded use cases →

Deductive reasoning — truth-preserving derivation

Deduction, the inheritance of Aristotle and classical logic, derives necessary conclusions from general rules plus specific facts. It is the only strategy in the family that is truth-preserving: if the premises hold and the chain is valid, the conclusion is not probable — it is entailed.

The graph shape reflects that severity: a strict linear chain, each node’s output the next node’s input, no branching. Phases run premise assembly, rule application, conclusion derivation, validity check — mapped to Retrieve (premises), Retrieve (rules), Apply, and Verify nodes. The gates are the two classical ones, made executable. The validity gate asks whether the premises are mutually consistent and the derivation well-formed. The soundness gate asks the harder question: are the premises actually true? A valid argument from a false premise is how a system produces a confidently wrong answer with perfect logical hygiene.

Deploy deduction for legal rule application, compliance checking, mathematical proof, and formal verification — domains where the rules are explicit and the cost of a leap is high. In our model-risk suites, this is the strategy underneath the formal-proof layer: every determination discharged as numbered propositions, each citing a rule, an evidence item, or a prior step.

Deep dive: how the deductive graph works, step by step, with three grounded use cases →

Inductive reasoning — generalization from instances

Induction, in the lineage of Hume and Mill, runs in the opposite direction from deduction: from specific instances toward a general pattern. Its conclusions are probabilistic by nature, and honest induction carries its confidence level with it.

The graph shape is many-to-one convergence: multiple evidence nodes feed a pattern-extraction stage, gated by sample sufficiency before any generalization is permitted. Phases run evidence gathering, pattern extraction, generalization, confidence assessment — mapped to Retrieve (instances, in parallel), Cluster, Abstract, and Evaluate (confidence) nodes. The gates target induction’s two classic failure modes. The sufficiency gate asks whether there are enough instances to support any generalization at all. The diversity gate asks whether the instances are varied enough — a thousand examples drawn from one corner of the distribution license far less than a hundred drawn across it.

Deploy induction for trend analysis, policy recommendation from case law, and learning from examples. The confidence-assessment node is not decoration: it is where the strategy binds its output to epistemic integrity, stating a conclusion and the evidential strength behind it, so downstream consumers — human or graph — know how much weight the generalization will bear.

Deep dive: how the inductive graph works, step by step, with three grounded use cases →

Three strategies, one discipline

Notice what the three specifications share. Each one turns a mode of inference that models perform implicitly — and inconsistently — into an explicit, gated, inspectable structure. An ungoverned LLM abduces, deduces, and induces constantly, in whatever mixture the token stream happens to produce, with no gate asking whether the observation was surprising, the premises were sound, or the sample was sufficient. Encoding the strategy as a graph does not make the model smarter. It makes the reasoning governed: every gate is a checkpoint an auditor can inspect, and every failure is caught where it occurs instead of surfacing as a confident conclusion three steps later.

Next in the series: the problem-solving family, starting with decomposition, means-ends analysis, and analogical reasoning.

The strategy library: series index

This index appears in every installment and tracks the inventory as the series covers it. The library currently catalogs nineteen strategies across seven families, drawn from epistemology, cognitive science, argumentation theory, philosophy of science, design thinking, linguistics, and professional practice — a starter library, extensible by the community, with more than twenty strategy configurations available on the platform.