Rules of Inference in Artificial intelligence
In this page we will learn about Rules of Inference in Artificial intelligence| Rules of Inference in Artificial intelligence | Types of Inference rules | Modus Ponens | Modus Tollens | Hypothetical Syllogism | Disjunctive Syllogism | Addition | Simplification | Resolution
Inference:
We need intelligent computers in artificial intelligence to construct new logic from old logic or evidence, therefore inference is the process of drawing conclusions from data and facts.
Inference rules:
The templates for creating valid arguments are known as inference rules. In artificial intelligence, inference rules are used to generate proofs, and a proof is a series of conclusions that leads to the intended outcome. The implication among all the connectives is vital in inference rules. Some terms relating to inference rules are as follows:
- Implication: It's one of the logical connectives, denoted by the letters P → Q. It's a Boolean expression, to be precise.
- Converse: The converse of implication is when the right-hand side statement is applied to the left-hand side, and vice versa. It is denoted by the letters Q → P.
- Contrapositive: Contrapositive is the negation of converse, and it can be expressed as ¬ Q → ¬ P.
- Inverse: Inverse is the antithesis of implication. ¬ P → ¬ Q can be used to symbolize it.
Some of the compound statements in the above term are equivalent to each other, which we can verify using the truth table:
P | Q | P → Q | Q → P | ¬ Q → ¬ P | ¬ P → ¬ Q |
---|---|---|---|---|---|
T | T | T | T | T | T |
T | F | F | T | F | T |
F | T | T | F | T | F |
F | F | T | T | T | T |
As a result from the above truth table, we can prove that P → Q is equivalent to ¬ Q → ¬ P, and Q→ P is equivalent to ¬ P → ¬ Q.
Types of Inference rules:
1. Modus Ponens:
One of the most essential laws of inference is the Modus Ponens rule, which asserts that if P and P → Q are both true, we can infer that Q will be true as well. It's written like this:
Example:
Statement-1: "If I am sleepy then I go to bed" ==> P → Q
Statement-2: ""I am sleepy" ==> P"
Conclusion: "I go to bed." ==> Q.
Hence, we can say that, if P → Q is true and P is true then Q will be true.
Proof by Truth table:
2.Modus Tollens:
According to the Modus Tollens rule if P→ Q is true and ¬ Q is true, then ¬ P will also true. It can be represented as:
Example:
Statement-1: "If I am sleepy then I go to bed" ==> P→ Q
Statement-2: "I do not go to the bed."==> ~Q
Statement-3: Which infers that "I am not sleepy" => ~P
Proof by Truth table:
3. Hypothetical Syllogism:
According to the Hypothetical Syllogism rule if P→R is true whenever P→Q is true, and Q→R is true. It can be represented as the following notation:
Example:
Statement-1: Statement-1: If you have my home key then you can unlock my home. P→Q
Statement-2: Statement-2: If you can unlock my home then you can take my money. Q→R
Statement-3: Conclusion: If you have my home key then you can take my money. P→R
Proof by Truth table:
4. Disjunctive Syllogism:
According to the Disjunctive syllogism rule if P∨Q is true, and ¬P is true, then Q will be true. It can be represented as:
Example:
Statement-1:Today is Sunday or Monday. ==>P∨Q
Statement-2:Today is not Sunday. ==> ¬P
Conclusion: Today is Monday. ==> Q
Proof by Truth table:
5. Addition:
According to the Addition rule which is one of the common inference rule, If P is true, then P∨Q will be true.
Example:
Statement-1: I have a vanilla ice-cream. ==> P
Statement-2: I have Chocolate ice-cream.
Conclusion: I have vanilla or chocolate ice-cream. ==> (P∨Q)
Proof by Truth table:
6. Simplification:
According to the simplification rule if P∧ Q is true, then Q or P will also be true. It can be represented as:
Proof by Truth table:
7. Resolution:
According to the Resolution rule if P∨Q and ¬ P∧R is true, then Q∨R will also be true. It can be represented as
Proof by Truth table:
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