Reasoning Glossary

If the premises are true and the inference rules are valid, the conclusion must be true.

Deduction where the proof object matters (what counts as a proof, how it's constructed).

A proof of existence must provide a construction/witness; some classical principles are restricted.

Transform expressions using equalities and rewrite rules while preserving meaning.

Reason by constructing/analyzing models that satisfy a theory (true in all models vs some).

Encode requirements as constraints and solve for assignments that satisfy them (or prove none exist).

Use types (including dependent/refinement types) to enforce invariants; "propositions as types" in some systems.

Propose an abstraction; check; if a counterexample appears, refine the abstraction and repeat.

Infer general patterns from observations ("observed many A are B -> probably A are B").

Inference about populations from samples via estimators, confidence intervals, tests, error rates.

Represent degrees of belief as probabilities and update them with evidence (Bayes' rule).

Generate multiple independent reasoning paths and find the consensus, reducing dependence on any single line of reasoning.

Compare how well hypotheses predict observed data via likelihoods, without necessarily committing to priors.

From observations, propose a hypothesis that would best explain them.

Generate many alternatives then evaluate ruthlessly. Separation of generation from evaluation -- quantity first, quality second.

Transfer relational structure from a known domain/case to a new one (often deeper than surface similarity).

Retrieve similar past cases and adapt their solutions.

Use an explanation of why a solution works to generalize a reusable rule/plan.

Prefer hypotheses that explain data with fewer assumptions / shorter descriptions, balancing fit vs complexity.

Predict by comparing to a base rate distribution of similar past projects/cases ("what usually happens?").

Rough quantitative estimates via decomposition and bounding.

Blend logical structure (relations/rules/quantifiers) with probabilistic uncertainty (e.g., probabilistic programming + constraints).

Represent uncertainty with ranges of probabilities when precision isn't justified.

Allocate "mass" to sets of possibilities; combine evidence into belief/plausibility intervals.

Choose distributions satisfying known constraints while assuming as little else as possible (maximize entropy).

Replace numeric probabilities with ordinal "degree of disbelief" ranks; update by shifting ranks.

Truth is a degree (0-1) because predicates have blurred boundaries ("tall," "near," "high risk").

More than two truth values; explicitly represent "unknown" or "undefined."

Approximate a concept by what is definitely in vs possibly in, given limited features/indiscernibility.

Categorize by similarity to prototypes/exemplars rather than strict necessary-and-sufficient definitions.

Reason with qualitative states ("increasing," "decreasing," "positive influence") instead of exact numbers.

Adding information can retract previous conclusions ("birds fly" until "penguin").

Use "normally/typically" rules overridden by more specific info.

Conclusions can be defeated by counterevidence or stronger rules; tracks priorities/strength.

Principles for revising an accepted belief set with new info, especially when inconsistent.

Tolerate contradictions without explosion (deriving everything).

Build arguments and counterarguments; compute which claims stand given attack/defense relations.

Structured argument that a system is acceptably safe/secure/reliable, supported by evidence and subclaims (often tree-like).

Identify causal relations and predict effects of interventions (distinguish P(Y|X) vs P(Y|do(X))).

Infer causal graph structure from data + assumptions (and ideally interventions).

Evaluate alternate histories given a causal model.

Explain/predict by identifying parts and interactions.

Infer hidden faults/causes from symptoms using a fault/causal model plus uncertainty handling.

Run an internal model (mental or computational) to predict consequences under scenarios.

Reason about interacting components over time: reinforcing/balancing loops, delays, unintended consequences.

From goals, derive actions/subgoals necessary or helpful to achieve them ("to get X, do Y").

Combine beliefs with preferences/utilities to choose actions (e.g., expected utility).

Decide with multiple objectives (cost, speed, safety, equity), often using weights, outranking, or Pareto frontiers.

Compute action sequences or policies achieving goals under constraints and dynamics.

Choose the best solution relative to an objective subject to constraints.

Choose actions that perform acceptably under worst plausible conditions or adversaries.

Choose the action minimizing worst-case regret (difference from best action in hindsight).

Seek a solution that is "good enough" given time/compute/info limits rather than globally optimal.

Decide which measurements/experiments reduce uncertainty most per cost to improve decisions.

Use simple rules that often work; fast but biased.

Systematically explore possibilities (tree search, dynamic programming), guided by heuristics and pruning.

Reason when outcomes depend on others' choices.

Infer beliefs, intentions, knowledge states of others (nested beliefs).

Reason about acceptable agreements and coalition formation under constraints and asymmetric information.

Design rules so that self-interested behavior leads to desired outcomes (align incentives).

Advance understanding through structured opposition: surface tensions, refine concepts, integrate perspectives.

Infer meaning and intent from language, documents, norms, artifacts using context and interpretive canons.

Build coherent time-ordered explanations connecting events, motives, causes into a story supporting prediction and action.

Decide "what kind of situation is this?" -- build frames that organize signals, priorities, and actions under ambiguity.

Reason with "necessarily," "possibly," "knows," and "after action X..." operators.

Reason about what is permitted, required, or forbidden; handle norm conflicts and exceptions.

Reason about ordering, duration, persistence, and change over time.

Reason using geometry/topology and often diagrams (containment, adjacency, flows).

A workflow: abduce hypotheses, deduce predictions, test (statistics), revise beliefs/theories.

Choose interventions, measurements, and sampling to identify effects (randomization, controls, blocking, instrumentation).

Iterate from requirements to architectures to prototypes with tradeoffs, constraints, and failure analyses.

Apply rules to facts, interpret texts, reason from precedents; uses burdens/standards of proof and adversarial argumentation.

Reason about right/wrong and value tradeoffs (consequentialist, deontological, virtue, contractualist, care ethics, etc.).

Reconstruct what happened from incomplete sources; triangulate evidence; assess credibility; compare hypotheses.

Blend pattern recognition (cases), mechanistic models, tests, triage, and risk constraints under time pressure.

Decide how to reason: which mode to use, effort allocation, what uncertainties matter, when to stop.

Track how reliable your beliefs are (forecast scoring, error bars, backtesting).

Iteratively adjust both principles and case judgments until they cohere.

Start from an accepted fact and infer what must be true for it to be possible (Kantian style).

Assume the role of an attacker/critic: try to break arguments, systems, incentives, and assumptions.

Structured checks to reduce predictable errors (base rates, alternative hypotheses, premortems, disconfirmation search).

Produce optimized search queries for finding primary sources and reviews.

Generate a plausible answer to improve retrieval -- you search for the shape of the answer, not just the question.

When intent is underspecified, find the single most useful question to ask.

In a multi-turn research session, find the question that most reduces remaining uncertainty.

Generate diverse question types to interrogate a topic from multiple angles.

Pull procedural knowledge out of a document as structured, sequenced steps.

Prevent missing key evidence buried in long documents.

Break a complex question into atomic subquestions with dependency ordering.

Build a structured evidence ledger -- claims, support, counterevidence, confidence.

When sources conflict, find principled reconciliation rather than ignoring the conflict.

Structured comparison of alternatives grounded in evidence, not impression.

Recover from a misunderstanding after feedback reveals the answer missed the point.

Maintain an explicit trace of exploration with branching and backtracking.

Steelman both sides of a contested question, then adjudicate.

Quality-gate a draft against evidence before publishing. Prevent overconfidence.

Plan a structured evidence search with inclusion criteria and gap identification.

Generate the minimal questions needed to clarify an underspecified problem.

Simulate advocates, critics, and judges to produce a balanced synthesis.

Produce structured claims with evidence, confidence, and narrative synthesis.

Plan the post's section structure before writing.

Control the range and variation of outputs -- narrow for precision, wide for exploration.

Draft an answer, then independently fact-check it before finalizing.

Trace which premises support which conclusions and identify where errors propagate.

Detect when a research or writing session is wandering from its goal.

Surface and challenge every assumption in an analysis.

Take stock of where the research/writing stands and what to do next.

Simulate a skeptical reviewer critiquing the draft.

Assess whether confidence levels in the analysis are warranted.