Reasoning Strategies, Part 2: The Problem-Solving Family

What this family is for

The epistemic strategies answer questions of belief: what explains this, what follows from that, what does the sample license. Problem-solving strategies answer a question of route: here is where we are, there is where we must end up — what sequence of moves connects them, and how would we know the sequence is sound? In regulated work the destination is usually written by someone else — a statute, a consent order, a policy, a filing clock — which makes the family less optional than it sounds. Most compliance work is pathfinding under someone else’s definition of done.

The family also shares a characteristic failure, and it is worth naming before the catalog. Unguided reasoning about goals produces plausible motion: steps that are individually sensible, locally productive, and collectively going nowhere — the remediation program that is busy but not closer, the deal restructured four times against four different rules, the plan that works on paper because nobody chained its prerequisites back to the present. Every gate in this family exists to catch some version of that failure: coverage gates that refuse conclusions with unanswered parts, progress gates that halt loops the moment an iteration closes nothing, grounding gates that reject plans whose prerequisite chains never touch today. The strategies differ in shape; the discipline — motion must be accountable to the goal — is the family trait.

Decomposition — split, solve, recompose

Decomposition, the oldest move in the methodical tradition — Descartes’ second rule, Pólya’s first question — splits one hard question into several answerable ones, answers each on its own evidence, and only then recomposes. The graph makes the split itself an explicit output: a dedicated node proposes the parts, each part is solved in its own scoped step that sees only its own evidence, and the recomposition is evaluated as a whole before an arbiter rules.

The coverage gate is the strategy’s contract: every named part answered, every answer evidenced, no aspect of the original question left orphaned between parts. The per-part scope gate buys independence — the answer to “was it timely?” cannot lean on the vibe of “was it authorized?”, because the step never sees it. Deploy it for element-by-element adjudication (a Reg E claim decomposes into the statute’s own elements), KYC files, and exam findings — anywhere a later challenge will land on one part and the answer must be correctable without redeciding everything.

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

Means-ends analysis — reduce the largest difference

Means-ends analysis, formalized by Newell and Simon in the General Problem Solver, is the oldest engineered reasoning loop there is: state the current state and the goal state, enumerate the differences, apply the operator that reduces the largest one, measure again. As a graph, the difference list is an explicit artifact — the loop’s working memory and its audit trail — and every proposed move must name which difference it reduces, or the gate throws it out as busy-work.

The signature is the progress gate: the loop runs only while iterations demonstrably shrink the list, and a full pass that closes nothing halts it — either the plan is done, or it is stuck, and a stuck plan routes to a human as stuck, not as “in progress.” Deploy it for consent-order and MRA remediation (the goal state is written by the regulator; the differences are the findings), case resolution against statutory clocks, and migration to a new rulebook, where the difference list doubles as the compliance mapping.

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

Analogical reasoning — structure over surface

Analogical reasoning solves a new case by mapping it onto a settled one — the engine of case law, policy application, and every experienced adjudicator’s “we had one just like this.” It is also the easiest strategy to do badly, because surface similarity masquerades as structural similarity, and next-token statistics reward exactly that confusion. The graph retrieves the precedent with its rationale, states the mapping feature by feature, and then runs the step that separates precedent-following from pattern-matching: a dedicated disanalogy critique that hunts for the differences that break the transfer.

The mapping gate admits a conclusion only with the mapping and the survived critique attached — the trace records not just “like March” but which features carried the likeness and which differences were weighed. And when no mapping survives, the honest output is “this case is genuinely new,” routed to a human as first-impression — the analogical graph’s form of abstention. Deploy it for precedent-consistent adjudication, policy application to novel fact patterns, and vendor-comparability claims in model risk.

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

Constraint satisfaction — every rule holds at once

Constraint satisfaction, from the CSP tradition in computer science, treats a decision as variables to assign under rules that must all hold simultaneously: enumerate the variables and their domains, retrieve every binding constraint with its source, propagate to prune what cannot work, and verify candidates against all of it — not the rule that spoke last. This is the cure for regulatory whack-a-mole: the deal that always almost works because the rules were consulted one at a time.

Two disciplines carry the strategy. Constraints are cited artifacts — a rule without a source is a preference wearing a uniform, and the enumeration gate rejects it. And the satisfaction gate treats an empty solution space as a first-class answer: infeasible, with the minimal conflicting set of constraints named, routed upward as an exception decision — instead of quietly relaxing whichever rule was in the way. Deploy it for structuring under policy and regulation, eligibility with interacting criteria, and conflicting-obligation analysis.

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

Working backward — from the goal to the given

Working backward is the ancients’ method of analysis — Pappus described it; Pólya revived it — run as a graph: fix the required end state, then chain prerequisites in reverse, each node asking “what must be true immediately before this?”, until the chain terminates in conditions already true today. Each link carries its real lead time, because lead times are where backward planning finds the deadlines nobody wrote down — the day-17 data request hiding inside a day-30 filing obligation.

The grounding gate enforces the whole point: a chain that never reaches the present is a wish, not a plan, and a chain whose earliest step lands last Tuesday is an infeasibility finding surfaced while escalation is still a choice. One boundary is built in: the strategy plans requirements, never conclusions. Working backward from “what must the file show” is evidence planning; working backward from “the answer we want” is the corruption the forward graph exists to prevent. Deploy it for statutory clocks, exam readiness, and evidence-sufficiency planning.

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

Five strategies, one discipline

As with the epistemic family, notice what the specifications share. An unguided model decomposes, subgoals, analogizes, juggles constraints, and plans backward constantly — implicitly, inconsistently, in whatever mixture the token stream produces, with no gate asking whether the parts covered the question, the iteration closed a difference, the precedent’s rationale actually transferred, every rule held at once, or the plan ever touched the present. Encoding the strategy as a graph does not make the model smarter. It makes the pathfinding governed: the goal is explicit, every move is accountable to it, and the failure modes — busy-work, surface matches, quietly bent rules, ungrounded plans — are caught at a named gate instead of surfacing as a confident plan that was never going to work.

With this release the Graph Library’s first three families — Epistemic, Problem-Solving, and Argumentative — are fully published: eleven graphs, each with its walkthrough, its gates specified operationally, and worked use cases. Next in the series: the scientific family — the hypothetico-deductive method and Bayesian updating.

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.