Inference is a good guess heuristics (based on logic, statistics etc.) to observations or by interpolating the next logical step in an intuited pattern. The conclusion drawn is also called an inference. The laws of valid inference are studied in the field of logic.
Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology;artificial intelligence researchers develop automated inference systems to emulate human inference. Statistical inference allows for inference from quantitative data.
Accuracy of inductive inferences
The process by which a conclusion is inferred from multiple observations is called inductive reasoning. The conclusion may be correct or incorrect, or correct to within a certain degree of accuracy, orcorrect in certain situations. Conclusions inferred from multiple observations may be tested by additional observations.
Examples of deductive inference
Greek philosophers defined a number of syllogisms, correct three part inferences, that can be used as building blocks for more complex reasoning. We begin with the most famous of them all:
1. All men are mortal
2. Socrates is a man
3.Therefore, Socrates is mortal.
The reader can check that the premises and conclusion are true, but Logic is concerned with inference: does the truth of the conclusion follow from that of the premises?
The validity of an inference depends on the form of the inference. That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference.An inference can be valid even if the parts are false, and can be invalid even if the parts are true. But a valid form with true premises will always have a true conclusion.
For example, consider the form of the following symbological track:
1. All apples are blue.
2. A banana is an apple.
3. Therefore, a banana is blue.
For the conclusion to be necessarily true, the premises need to betrue.
Now we turn to an invalid form.
1. All A are B.
2. C is a B.
3. Therefore, C is an A.
To show that this form is invalid, we demonstrate how it can lead from true premises to a false conclusion.
1. All apples are fruit. (True)
2. Bananas are fruit. (True)
3. Therefore, bananas are apples. (False)
A valid argument with false premises may lead to a false conclusion:
1. All fatpeople are Greek.
2. John Lennon was fat.
3. Therefore, John Lennon was Greek.
When a valid argument is used to derive a false conclusion from false premises, the inference is valid because it follows the form of a correct inference.
A valid argument can also be used to derive a true conclusion from false premises:
1. All fat people are musicians
2. John Lennon was fat
3. Therefore,John Lennon was a musician
In this case we have two false premises that imply a true conclusion.
An incorrect inference is known as a fallacy. Philosophers who study informal logic have compiled large lists of them, and cognitive psychologists have documented many biases in human reasoning that favor incorrect reasoning.
Automatic logical inference
AI systems first providedautomated logical inference and these were once extremely popular research topics, leading to industrial applications under the form of expert systems and later business rule engines.
An inference system's job is to extend a knowledge base automatically. The knowledge base (KB) is a set of propositions that represent what the system knows about the world. Several techniques can be used by thatsystem to extend KB by means of valid inferences. An additional requirement is that the conclusions the system arrives at are relevant to its task.
Example using Prolog
Prolog (for "Programming in Logic") is a programming language based on a subset of predicate calculus. Its main job is to check whether a certain proposition can be inferred from a KB (knowledge base) using an algorithm called...
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