Direct answer
Counterexample, in this definition, is limited to the following inspected scope. A counterexample to entailment is a case where premises are true and the conclusion false. The answer carries the source boundaries forward and does not infer authority from a neighboring topic.
Definition
Use the term only for the source-backed scope stated here; keep adjacent concepts separate unless a typed relationship is explicit.
A useful definition states both inclusion and exclusion conditions so a machine answer cannot silently widen it.
Applied scope: A counterexample to entailment is a case where premises are true and the conclusion false.
Definition and operating context
The canonical concept owner is maha-research. This route may apply evidence; it cannot redefine or inherit the authority of its canonical owner.
This property may publish research objects, machine-readable provenance, reproduction protocols. It must not publish sales copy or unsupported interpretation.
Evidence and exact locators
forall x: Calgary — An Introduction to Formal Logic — Chapter 2, validity and counterexample cases. Establishes: A counterexample to entailment is a case where premises are true and the conclusion false.
What the evidence does not establish
One counterexample refutes the corresponding universal or entailment claim; it does not establish a replacement theory or refute a narrower claim.
This route must not claim sales copy.
This route must not claim unsupported interpretation.
Related definitions and applications
graphEdges: https://research.mahastrategies.com/federation/research/source-identity/definition
same-topic-application: https://research.mahastrategies.com/federation/research/counterexample/fixture
same-topic-application: https://research.mahastrategies.com/federation/research/counterexample/relationships
same-topic-application: https://research.mahastrategies.com/federation/research/counterexample/method
property-home: https://research.mahastrategies.com/
same-topic-application: https://research.mahastrategies.com/federation/research/counterexample/protocol
Questions this page can answer
What does Counterexample mean in this bounded context?
Counterexample, in this definition, is limited to the following inspected scope. A counterexample to entailment is a case where premises are true and the conclusion false. The answer carries the source boundaries forward and does not infer authority from a neighboring topic.
Which inspected sources support this definition answer?
forall x: Calgary — An Introduction to Formal Logic (current CC BY edition inspected 2026-09-06), at Chapter 2, validity and counterexample cases, supports a counterexample to entailment is a case where premises are true and the conclusion false.
What does the evidence not establish?
One counterexample refutes the corresponding universal or entailment claim; it does not establish a replacement theory or refute a narrower claim. Property boundary: This route may apply evidence; it cannot redefine or inherit the authority of its canonical owner.
Which definition or canonical owner must be read first?
This page is the local maha-research definition for its topic. Related applications may depend on it but may not silently redefine it.
What source, policy, implementation, or release change would require revision?
Re-evaluate this page when a cited source, locator, governing instrument, local implementation, or canonical definition changes. Publication also requires a matching exact-revision review and active canonical release.