The closed world assumption (CWA) is the presumption that what is not currently known to be true is false. The same name also refers to a logical formalization of this assumption by Raymond Reiter. The opposite of the closed world assumption is the open world assumption (OWA), stating that lack of knowledge does not imply falsity. Decisions on CWA vs. OWA determine the understanding of the actual semantics of a conceptual expression with the same notations of concepts. A successful formalization of natural language semantics usually can not avoid an explicit revelation of the implicit logical backgrounds based on whether CWA or OWA.
Negation as failure is related to the closed world assumption, as it amounts to believing false every predicate that cannot be proved to be true.
In the knowledge management arena, the closed world assumption is used in at least two situations: 1) when the knowledge base is known to be complete (e.g., a corporate database containing records for every employee), and 2) when the knowledge base is known to be incomplete but a "best" definite answer must be derived from incomplete information. For example, if a database contains the following table reporting editors who have worked on a given article, a query on the people not having edited the article on Formal Logic is usually expected to return “Sarah Johnson”.
| Edit | |
|---|---|
| Editor | Article |
| John Doe | Formal Logic |
| John Doe | Closed World Assumption |
| Joshua A. Norton | Formal Logic |
| Sarah Johnson | Introduction to Spatial Databases |
| Charles Ponzi | Formal Logic |
| Emma Lee-Choon | Formal Logic |
In the closed world assumption, the table is assumed to be complete (it lists all editor-article relationships), and Sarah Johnson is the only editor who has not edited the article on Formal Logic. In contrast, with the open world assumption the table is not assumed to contain all editor-article tuples, and the answer to who has not edited the Formal Logic article is unknown. There is an unknown number of editors not listed in the table, and an unknown number of articles edited by Sarah Johnson that are also not listed in the table.
Read more about Closed World Assumption: Formalization in Logic
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