DL discussion

Open-world vs closed-world, SQL examples, universal quantification and empty extensions

The open-world assumption (OWA) treats a statement as possibly true even if not known to be true; the closed-world assumption (CWA) is often glossed as: what is not known true is false. The canonical page quotes Wikipedia and a small example: given “Mary is a citizen of France”, whether Paul is a citizen of France is unknown under OWA and “no rows” under a naïve SQL reading — but the text argues that a SQL query returning zero rows is better read as unknown than as a logical “No”, so simplistic OWA-vs-CWA slogans can mislead practice.

The discussion in [ArSm2015] (example tables around “CWA0”) is cited on taoke.de as similarly easy to misread when column names and intended semantics are ambiguous.

Another theme is when application expectations diverge from DL semantics — e.g. diagrams “person with or without gender” and “person with or without children” (figures person-gender, person-child on taoke.de). ∀R.C is vacuously satisfied when there are no R-successors, which surprises many modellers until the open-world reading of roles is internalised.

The TAoKE page recommends focusing on the intended meaning of models and implementations rather than only on textbook OWA/CWA labels — a stance relevant when you map DL-style rules to deriver.app sessions where defaults and closed-world checks may be mixed explicitly in rules.