Nonmonotonic Reasoning

Nonmonotonic Reasoning

As was explained in Section seven.18, formal logic and predicate logic square measure monotonic reasoning systems. this implies that if a conclusion C could also be derived from a bunch of expressions, S, then any vary of additional expressions being further to S cannot modification the fact value of C, provided the expressions in S keep consistent.
In different words, a monotonic reasoning system that stores realitys concerning the world can deduce new realitys from its existing facts but would never have cause to delete or modify associate existing fact (unless the world changed).
Hence, the number of facts the system stores will increase monotonically.

In world, reasoning tends to not be so simple. as associate degree example, you’ll grasp that dogs like better to eat meat, that Fido could also be a dog. Hence, you conclude that Fido will like better to eat meat. If you are later enlightened that Fido could also be a eater dog, you will ought to modification your conclusion. this kind of reasoning is known as nonmonotonic reasoning.
A nonmonotonic reasoning system needs to be able to wound the actual fact that conclusions modification as new facts square measure introduced and, hence, that its data is not ceaselessly positive as a results of later facts may contradict it. throughout this context, we have a tendency to frequently use the word “belief” rather than “fact” to elucidate things of information that the system stores or deduces concerning the world.
In this section, we’ve a bent to introduce kind of systems and principles that square measure accustomed wound nonmonotonic reasoning things.

1 – nonmonotonic Logic with the Modal Operator, M

One way to reason in nonmonotonic things is to use nonmonotonic logic. This involves augmenting the predicate calculus with a modal opera￾tor, M, that’s used to represent the thought that associate degree announcement is per all our beliefs. Hence, we might write

∀x bird (x) ∧ M flies (x) → flies (x)

This can be scan as follows:“for all x,if x could also be a bird and it’s per per to believe that x can fly, then x can fly.” in numerous words, most birds can fly.
We would accept M flies (x) to be false if we’ve a bent to already knew that the bird was dead and, in addition, we’ve a bent to knew that dead birds could not fly. Note that we have merely delineate a nonmonotonic logic, that’s used is utilized reasoning.

2 – Default Reasoning

Default reasoning is another kind of nonmonotonic reasoning that involves forward positive statements to be true, unless there is some clear proof to the contrary. this is {often|this can be} often a spread of reasoning that folk use all the time. as associate degree example, a automobile could drive past you too fast for you to see whether or not or not it is a driver or not. it might be reasonable for you to assume that the auto contains a driver, unless you happen to understand that it’s it’s automobile, otherwise you saw the driver appear previously. this is {often|this can be} usually this can be often, as a result of it assumes positive facts by default, unless they are disproved by another facts.
A notation like that delineate in Section seventeen.6.1 is utilized for default logic:

Car (x) ∧ :Has_Driver (x) → Has_Driver (x)

This is a default rule, that states, in default logic notation, that if x could also be a automobile, and it’s per our beliefs to believe that x contains a driver, then {we can|we’ll|we are going to} conclude that x will thus have a driver.
Similarly, the sentence on top of is scan as “if x could also be a automobile and there’s no reason to suppose that x does not have a driver, then conclude that x can have a driver.”

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