{{no footnotes, date=October 2016 In nonmonotonic reasoning, the Nixon diamond is a scenario in which default assumptions lead to mutually inconsistent conclusions. The scenario is: * usually,

Quakers Quakers are people who belong to a historically Protestant Christian set of denominations known formally as the Religious Society of Friends. Members of these movements ("theFriends") are generally united by a belief in each human's abil ...

are

pacifist Pacifism is the opposition or resistance to war, militarism (including conscription and mandatory military service) or violence. Pacifists generally reject theories of Just War. The word ''pacifism'' was coined by the French peace campaign ...

* usually,

Republicans Republican can refer to: Political ideology * An advocate of a republic, a type of government that is not a monarchy or dictatorship, and is usually associated with the rule of law. ** Republicanism, the ideology in support of republics or agains ...

are not pacifist *

Richard Nixon Richard Milhous Nixon (January 9, 1913April 22, 1994) was the 37th president of the United States, serving from 1969 to 1974. A member of the Republican Party, he previously served as a representative and senator from California and was ...

is both a Quaker and a Republican Since Nixon is a Quaker, one could assume that he is a pacifist; since he is Republican, however, one could also assume he is not a pacifist. The problem is how a

formal logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

of nonmonotonic reasoning should deal with such cases. Two approaches can be adopted: ; skeptical : since Nixon can neither be proved to be a pacifist nor the contrary, no conclusion is drawn; ; credulous : since Nixon can be proved to be a pacifist in at least one case, he is believed to be a pacifist; however, since he can also be proved not to be a pacifist, he is also believed not to be a pacifist. The credulous approach can allow proving both something and its contrary. For this reason, the skeptical approach is often preferred. Another solution to this problem is to attach priorities to default assumptions; for example, the fact that “usually, Republicans are not pacifist” can be assumed more likely than “usually, Quakers are pacifist”, leading to the conclusion that Nixon is not pacifist. The name ''diamond'' comes from the fact that such a scenario, when expressed as a belief network, forms a

diamond shape In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The ...

. This example is mentioned for the first time by Reiter and Criscuolo in a slightly different form where the person that is both a Republican and a Quaker is a John instead of Richard Nixon.

References

* W. Marek and M. Truszczynski (1993). ''Nonmonotonic Logics: Context-Dependent Reasoning''. Springer. * R. Reiter and G. Criscuolo (1981). On interacting defaults. In '' Proceedings of the Seventh International Joint Conference on Artificial Intelligence (IJCAI'81)'', pages 94–100.

External links

Review of John Horty paper on Floating Conclusions
Non-classical logic

See also

References

External links