Inference Logic
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Inference Inference Assuming what will happen. Not a conclusion, a prediction or hypothesis. A conclusion based on premise •
Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology.
•
Logic studies the laws of valid inference.
•
Statisticians have developed formal rules for inference (statistical inference) from quantitative inference mean booty data.
•
Artificial intelligence researchers develop automated inference systems.
The accuracy of inductive and deductive inferences
Deductive The process by which a conclusion is logically inferred from certain premises is called deductive reasoning. Mathematics makes use of deductive inference. Certain definitions and axioms are taken as a starting point and from these certain theorems are deduced using pure reasoning. The idea for a theorem may have many sources: analogy, pattern recognition, and experiment are examples of where the inspiration for a theorem comes from. However, a conjecture is not granted the status of theorem until it has a deductive proof. This method of inference is even more accurate than the scientific method. Mistakes are usually quickly detected by other mathematicians and corrected. The proofs of Euclid, for example, have mistakes in them that have been caught and corrected, but the theorems of Euclid, all of them without exception, have stood the test of time for more than two thousand years.
Valid inferences Inferences are either valid or invalid, but not both. Philosophical logic has attempted to define the rules of proper inference, i.e. the formal rules that, when correctly applied to true premises, lead to true conclusions. Aristotle has given one of the most famous statements of those rules in his Organon. Modern mathematical logic, beginning in the 19th century, has built numerous formal systems.
Inductive 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, or correct in certain situations. Conclusions inferred from multiple observations may be tested by additional observations.
Example of deductive inference Greek philosophers defined a number of syllogisms, correct three-part inferences, which can be used as building blocks for more complex reasoning. We'll begin with the most famous of them all: All men are mortal Socrates is a man ------------------
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.
Incorrect inference 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 provided automated 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 that system to extend KB by means of valid inferences. An additional requirement is that the conclusions the system arrives at are relevant to its task
http://en.wikipedia.org/wiki/Inference
ARTICLE#5
NAME:
VINOD KUMAR
STUDENT ID:
SP07-BB-0177
SUBJECT:
INTRO TO LOGIC
SECTION:
”B”
SUBMIT TO:
DR: SHAFQAT BHUKHARI
DATE:
03/10/2009
Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology.
•
Logic studies the laws of valid inference.
•
Statisticians have developed formal rules for inference (statistical inference) from quantitative inference mean booty data.
•
Artificial intelligence researchers develop automated inference systems.
The accuracy of inductive and deductive inferences
Deductive The process by which a conclusion is logically inferred from certain premises is called deductive reasoning. Mathematics makes use of deductive inference. Certain definitions and axioms are taken as a starting point and from these certain theorems are deduced using pure reasoning. The idea for a theorem may have many sources: analogy, pattern recognition, and experiment are examples of where the inspiration for a theorem comes from. However, a conjecture is not granted the status of theorem until it has a deductive proof. This method of inference is even more accurate than the scientific method. Mistakes are usually quickly detected by other mathematicians and corrected. The proofs of Euclid, for example, have mistakes in them that have been caught and corrected, but the theorems of Euclid, all of them without exception, have stood the test of time for more than two thousand years.
Valid inferences Inferences are either valid or invalid, but not both. Philosophical logic has attempted to define the rules of proper inference, i.e. the formal rules that, when correctly applied to true premises, lead to true conclusions. Aristotle has given one of the most famous statements of those rules in his Organon. Modern mathematical logic, beginning in the 19th century, has built numerous formal systems.
Inductive 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, or correct in certain situations. Conclusions inferred from multiple observations may be tested by additional observations.
Example of deductive inference Greek philosophers defined a number of syllogisms, correct three-part inferences, which can be used as building blocks for more complex reasoning. We'll begin with the most famous of them all: All men are mortal Socrates is a man ------------------
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.
Incorrect inference 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 provided automated 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 that system to extend KB by means of valid inferences. An additional requirement is that the conclusions the system arrives at are relevant to its task
http://en.wikipedia.org/wiki/Inference
ARTICLE#5
NAME:
VINOD KUMAR
STUDENT ID:
SP07-BB-0177
SUBJECT:
INTRO TO LOGIC
SECTION:
”B”
SUBMIT TO:
DR: SHAFQAT BHUKHARI
DATE:
03/10/2009
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