Nonmonotonic Logic

When Logical Conclusions Do Not Hold True

Inference rules are called nonmonotonic when they allow intelligent systems ‘to augment their beliefs by new ones that do not logically follow from their explicit ones” and this or another inference may have to be retracted.

Ordinary inference rules are monotonic “because the set of theorems derivable from premises is not reduced by adding to the premises.” 

… from Logical foundations of artificial intelligence by MR Genesereth and NJ Nilsson (1987)

"Consider putting an axiom in a common sense database asserting that birds can fly. Clearly the axiom must be qualified in some way since penguins, dead birds and birds whose feet are encased in concrete can't fly. A careful construction of the axiom might succeed in including the exceptions of penguins and dead birds, but clearly we can think up as many additional exceptions like birds with their feet encased in concrete as we like. Formalized nonmonotonic reasoning [citations] provides a way of saying that a bird can fly unless there is an abnormal circumstance and reasoning that only the abnormal circumstances whose existence follows from the facts being taken into account will be considered."
 - Nonmonotonicity section of John McCarthy's Generality in Artificial Intelligence (1971-1987).


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