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The open world assumption or OWA recognises that knowledge of the world is incomplete. If something cannot be proved to be true, then it doesn't automatically become false. In the OWA, what is not stated is considered unknown, rather than wrong.

Statement: "Mary" "is a citizen of" "France"
Question: Is Mary a citizen of Canada?

  • "Closed world" (for example SQL-based dbms's) answer: No.
  • "Open world" answer: unknown (Mary could have dual citizenship).

    Under the OWA, failure to derive a fact does not imply the opposite. For example, assume we only know that Mary is a citizen of France. From this information we can neither conclude that Mary is not a citizen of Canada, nor that she is. Therefore, we admit the fact that our knowledge of the world is incomplete. The open world assumption is closely related to the monotonic nature of first-order logic: adding new information never falsifies a previous conclusion. Thus, if we subsequently learn that Mary is also a citizen of Canada, this does not change any earlier positive or negative conclusions. It can merely replace 'unknown' conclusions by definitive 'true' or 'false' conclusions.


    In contrast, the CLOSED WORLD ASSUMPTION is as follows:-

    The closed world assumption is the presumption that what is not currently known to be true is false. The opposite of the closed world assumption is the open world assumption, stating that lack of knowledge does not imply falsity.

    Negation as failure is related to the closed world assumption, as it amounts to believing to be 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'.

    Editor Article
    John Doe Formal Logic
    John Doe Joshua A. Norton
    Sarah Johnson Charles Ponzi
    Emma Lee-Choon Formal Logic

    The current narrow theoretical interpretation of the relational database model (the version espoused by Date, Darwen, and Pascal) relies explicitly upon the Closed World Assumption

    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 (i.e. Sarah Johnson plus an unknown number of others). There is an unknown number of editors not listed in the table, and also an unknown number of articles edited by Sarah Johnson that are not listed in the table.


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