---
title: "Closed-world assumption"
type: "entity"
entity_kind: "concept"
status: "hub"
canonical_name: "closed-world assumption"
aliases: ["closed-world reasoning","CWA","negation as failure","negation-as-failure"]
first_seen: "2026-07-12T00:00:00.000Z"
writer_model: "claude-opus-4-8"
connects_to: ["non-monotonic reasoning","default logic","negation as failure","conditional reasoning","Answer Set Programming"]
seek_code_commit: "a619c8a"
---


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 [[entity-raymond-reiter|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**: [[entity-keith-stenning|Stenning]] and [[entity-michiel-van-lambalgen|van Lambalgen]] model the [[entity-peter-wason|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
- [[claim-conditional-reasoning-fallacies-as-closed-world-inference-in-asp]] · [[claim-stenning-van-lambalgen-model-wason-fallacies-as-closed-world-reasoning]] · [[claim-stenning-van-lambalgen-two-clause-exception-scheme-not-material-conditional]] · [[claim-stenning-van-lambalgen-do-not-use-negation-as-failure-in-2001-2004-papers]] · [[claim-logic-programming-account-rivals-probabilistic-account-of-conditional-reasoning]]
- Captures: 2026-08-31-do-stenning-van-lambalgen-actually-model-the-wason