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

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 ∧ ∼ ab_a.

where ab_a is an atom that means abnormal with respect to some aspect a. Given c, the agent can infer bunless it is told ab_a. Adding ab_a to the knowledge base can prevent the conclusion of b. Rules that imply ab_acan be used to prevent the default under the conditions of the body of the rule.