Logical Thinking

Produce the strongest conclusion the available premises warrant, including unknown, conditional, or no conclusion when appropriate. Logical rigor means choosing the right inference system, preserving meaning and scope, checking each decisive step, and refusing to strengthen the result beyond its proof obligations.

Scale the proof to the question

Adapt the inference family; do not impose a universal template. Preserve meaning, units, scope and quantifiers. Test whether premises can hold while the conclusion fails; use decisive calculations, solvers, tests or observations. Correlated self-review is not independent verification.

For consequential, multi-step, ambiguous or contested inference, read proof and verification plus the applicable family below for maps, step checks, conclusion types and adversarial tests. Simple entailment/calculation remains direct.

Use conditional or unknown when warranted. Proven, must, causes, always and impossible require their own proof burden.

Normalize the problem

Before inference, identify:

• exact question and candidate conclusion;
• premises, observations, rules, and documentation;
• source/status of each premise: given, observed, documented, inferred, assumed, or disputed;
• definitions, entities, variables, units, timeframe, version, and domain;
• quantifiers and modal force: all, some, none, must, may, usually, likely;
• knowledge regime: closed world, open world, or incomplete real-world evidence;
• hidden premises required to connect the stated information.

Resolve semantic ambiguity before formalizing. Do not create precision by translating an unclear sentence into symbols without deciding what the sentence means.

Choose the inference family

Family	Appropriate question	Valid conclusion form
Deductive	Must the conclusion follow?	entailed, contradicted, or unknown
Defeasible/informal	Is the argument presumptively reasonable?	supported unless a critical exception succeeds
Inductive	How strongly do observations generalize?	scoped probability or empirical support
Abductive	Which explanation best accounts for the evidence?	best current explanation, not proof
Causal	What would happen under intervention or counterfactual change?	association, intervention effect, or counterfactual claim
Probabilistic	How should uncertainty update?	posterior or calibrated range under assumptions
Documentary/rule	What does an authority establish here?	governing, permitted, required, documented, or unresolved applicability
Decision	Which action is preferable under uncertainty?	recommendation conditional on goals and tradeoffs

For formal entailment, natural-language arguments, exceptions, or scheme-based reasoning, read formal and defeasible inference.

For causal, probabilistic, forecasting, or decision reasoning, read causal, probabilistic, and decision reasoning.

For conclusions from documentation, policies, tests, benchmarks, source code, or runtime evidence, read documentation and evidence conclusions.

Keep unknown open

Under an open-world or incomplete-evidence regime:

• failure to prove C does not prove not C;
• failure to prove not C does not prove C;
• one absent fact does not license a closed-world assumption unless the system explicitly defines one;
• inconsistent premises do not justify an arbitrary conclusion in ordinary analysis.

Classify a deductive target as:

• Entailed: every model satisfying the premises satisfies C.
• Contradicted: every model satisfying the premises satisfies not C, or C directly conflicts with a controlling premise.
• Unknown: both C and not C remain compatible with the premises.
• Premises inconsistent: the premise set itself requires repair before ordinary inference.

Check premise consistency first, then classify the target as entailed, contradicted or unknown; do not force a binary answer from incomplete evidence.

Coordinate boundaries

Use critical-thinking when the central question is whether evidence, assumptions, incentives, or argument quality deserves confidence. Use evidence-reconciliation when conflicting authority or current source state controls. Use deep-research when premises must be discovered. Use creativity when the missing work is generating possibilities rather than adjudicating what follows.

Deliver

For simple problems, apply the protocol silently and answer directly. For consequential problems, report the normalized premises, inference family, decisive rule or test, exceptions or unknowns, verification performed, and strongest warranted conclusion. Show enough structure to audit the result without dumping private scratch reasoning.