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[MCS-003] Write a note on Non-monotonic reasoning systems.

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Non-monotonic Reasoning

The definite clause logic is monotonic in the sense that anything that could be concluded before a clause is added can still be concluded after it is added; adding knowledge does not reduce the set of propositions that can be derived.
A logic is non-monotonic if some conclusions can be invalidated by adding more knowledge. The logic of definite clauses with negation as failure is non-monotonic. Non-monotonic reasoning is useful for representing defaults. A default is a rule that can be used unless it overridden by an exception.
For example, to say that b is normally true if c is true, a knowledge base designer can write a rule of the form
b ←c ∧ ∼ aba.
where aba is an atom that means abnormal with respect to some aspect a. Given c, the agent can infer bunless it is told aba. Adding aba to the knowledge base can prevent the conclusion of b. Rules that imply abacan be used to prevent the default under the conditions of the body of the rule.


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