Introduction to Reasoning with Uncertain Knowledge:
Reasoning probably brings to mind logic puzzles, but it is something which we do every day of our lives. Reasoning in AI is the process by which we use the knowledge we have to draw conclusions or infer something new about a domain of interest. It is necessary part of what we call “intelligence”. Without the ability to reason we are doing little more than a lookup when we use information.
In fact, this is the difference between a standard data base system and a knowledge base. Both have information which can be accessed in various ways but the data base, unlike the knowledge base in the expert system, has no reasoning facilities and can therefore answer only limited specific questions.
What are the types of reasoning we come across? How do we know what to expect when we go on a train journey? What do we think when our friend is annoyed with us? How do we know what will happen if our car has a flat battery? Whether we are aware of it or not, we will use a number of different methods of reasoning, depending on the problem we are considering and the information that we have before us.
The three everyday situations mentioned above illustrate three key types of reasoning which we use. In the first case we know what to expect on a train journey because of our experience of numerous other train journeys. We infer that the new journey will share common features with the examples.
We are aware of the first example called induction, which can be summarised as generalisation from cases seen to infer information about cases unseen. We use it frequently in learning about the world around us. For example, every crow we see is black; therefore we infer that all crows are black. If we think about it, such reasoning is unreliable, we can never prove our inferences to be true, we can only prove them to be false. Take the crow again.
To prove that all crows are black we would have to confirm that all crows which exist, have existed or will exist are black. This is obviously not possible. However, to disprove the statement, all we need is to produce a single crow which is white or pink.
So at best we can amass evidence to support our belief that all crows are black. In spite of its unreliability inductive reasoning is very useful and is the basis of much of our learning. It is used particularly in machine learning.
The second example we considered was working out why a friend is annoyed with us, in other words trying to find an explanation for our friend’s behaviour. It may be that this particular friend is a stickler for punctuality and we are a few minutes late to our rendezvous. We may therefore infer that our friend’s anger is caused by we being late.
This is abduction, the process of reasoning back from something to the state or event which caused it. Of course this too is unreliable; it may be possible that our friend is angry for some other reason (perhaps we had promised to telephone him before coming to him but had avoided). Abduction can be used in cases where the knowledge is incomplete, Abduction can provide a “best guess” given, the available evidence.
The third problem is usually solved by deduction: we have knowledge about cars such as “if the battery is flat the headlights won’t work”; we know the battery is flat so we can infer that the lights won’t work. This is the reasoning of standard logic.
Indeed, we would express our car problem in terms of logic given that:
a = the battery is flat and b = the lights won’t work and the axioms
ᗄx: a(x) → b(x)
a (my car).
We can deduce b the light of my car won’t work (my car).
However, we cannot deduce the inverse: that is if we know b, we cannot deduce a; the battery of my car is flat if the lights of my car won’t work. This is not permitted in standard logic. If lights don’t work we may use abduction to derive this explanation. However, it could be wrong; there may be another explanation for the light failure (for example, a bulb may have blown or the battery connections may be loose).
Deduction is probably the most familiar form of explicit reasoning. It can be defined as the process of driving the logically necessary conclusion from the initial premises.
For example:
Elephants are bigger than dogs
Dogs are bigger than mice
Therefore
Elephants are bigger than mice
However, it should be noted that deduction is concerned with logical validity, not actual truth.
Consider the following example; given the facts, can we reach the conclusion by deduction?
Some dogs are greyhounds
The greyhounds run fast
Therefore
Some dogs run fast.
The answer is no. We cannot make this deduction because we do not know that all greyhounds are dogs. The fast dogs may therefore be the greyhounds which are not dogs. This of course is non-sensual in terms of what we know (or more accurately have induced) about the real world, but it is perfectly valid based on the premises given. We should therefore be cautious: deduction (also called analogical inference) does not always correspond to natural human (common sense) reasoning.
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