Nixon diamond

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The Nixon Diamond ( English: Nixon diamond ) denotes a known example scenario from the Artificial Intelligence . It mostly serves to illustrate consistency-preserving knowledge processing, occasionally also to clarify different knowledge representation mechanisms .

term

The term can be traced back to the graphic representation of the scenario, which is reminiscent of a diamond . It comes from the English where "diamond" stands for both "rhombus" and " diamond ". Because of this multiple meaning, "Nixon diamond" is sometimes incorrectly translated as "Nixon diamond".

scenario

The following initial knowledge is given:

  1. Nixon is a Quaker .
  2. Nixon is a Republican .
  3. Quakers are pacifists.
  4. Republicans are not pacifists.

interpretation

Classic logic

If we understand the above statements as theorems of classical propositional or predicate logic , we can deduce from 1. and 3. that Nixon is a pacifist. On the other hand, we can deduce from 2. and 4. that Nixon is not a pacifist. The given knowledge is therefore contradictory, the corresponding logical theory inconsistent.

Non-monotonous interpretation

As an alternative to the above point of view, it is obvious to understand the last two sentences as prototypical rules that merely describe a typical pattern. This can be underlined by the adverb "normally":

  1. Nixon is a Quaker.
  2. Nixon is a Republican.
  3. Quakers are usually pacifists.
  4. Republicans are not usually pacifists.

Such an interpretation provides two different consistent worldviews that allow a statement about Nixon's inclination to pacifism: In one, Nixon is a pacifist, which can be justified by Nixon's Quakerism and the pacifism typical of Quakers. In the other, Nixon is not a pacifist, which can be justified by Nixon's Republican inclination and typical Republican anti-pacifism. Possible inconsistent worldviews, in which Nixon is both a pacifist and a non-pacifist, are usually not considered.

See also

literature

  • Stuart Russell, Peter Norvig : Artificial Intelligence: A Modern Approach , 2nd edition, 2002, Prentice Hall. (German: Artificial Intelligence: A Modern Approach , August 2004, Pearson Studies, 2nd Edition, ISBN 3-8273-7089-2 , p. 445)
  • Christoph Beierle, Gabriele Kern-Isberner: Methods of knowledge-based systems: fundamentals, algorithms, applications. Teubner-Verlag, 2006, p. 263.