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Closed-world assumption

The closed-world assumption (CWA) is the non-monotonic inference rule that any statement not known (or not provable) to be true is taken to be false — "believe false what cannot be proved." It was formalized for incomplete databases by Raymond Reiter in 1978 and is close kin to default logic and to the closely related logic-programming operator negation as failure (NAF), which realizes the same idea as a proof procedure: a goal is taken as false when every attempt to prove it fails finitely. (NAF and CWA are distinct — one an operator, one an assumption about a knowledge base — but tightly coupled; the vault treats NAF here rather than as its own hub.)

The concept is load-bearing across this vault's reasoning cluster in two ways. First, as AI machinery: Sakama realizes human conditional-reasoning "fallacies" as closed-world completion in Answer Set Programming, grounded in Reiter's default logic (claim-conditional-reasoning-fallacies-as-closed-world-inference-in-asp). Second, as a cognitive model: Stenning and van Lambalgen model the Wason-task readings as closed-world, non-monotonic reasoning in their own words (claim-stenning-van-lambalgen-model-wason-fallacies-as-closed-world-reasoning), via a two-clause exception scheme (claim-stenning-van-lambalgen-two-clause-exception-scheme-not-material-conditional). A live terminological finding: S&vL reach the CWA idea without the "negation as failure" label, which is Sakama's later gloss (claim-stenning-van-lambalgen-do-not-use-negation-as-failure-in-2001-2004-papers).

References

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