Propositional Logic in Artificial Intelligence

Logic:

Logic defined as a formal system in which the formulae or sentences have true or false values. In 1976, Robert Kowalski invented this Propositional Logic following equation:

Algorithm = Logic + Control

The logic component specifies the knowledge to be used in solving problems. The control component determines the problem-solving strategies through which that knowledge used.

Propositional Logic:

Propositions are statements used in mathematics. A proposition or sentence is classified as declarative sentence whose value is either ‘true‘ or ‘false‘.

Example:
i. The sky is blue.
ii. Snow is white
iii. 2+2=4

Propositions are of two types –
1. Atomic Propositions: It is single propositions.
Example: The sky is blue.

2. Molecular Propositions: It is formed by combining two or more atomic propositions.
Example: “Sachin Tendulkar is a Cricketer and Roger Federer is a Tennis Player”.

Note: The logic component determines the meaning of the algorithm whereas the control component only affects its efficiency. In reasoning about truth values, we use a number of operators like:

In reasoning, there are five types of operators.
1. Not Operator: It is a unary operator. It applied only to one variable.

2. And Operator: It is a binary operator. It acts on two variables. It is also called a conjunctive operator.

3. Or Operator: It is also a binary operator. It also called a disjunctive operator.

4. Implies Operator: Its truth table is as follows:

In the following statement,
[c]
A->B
‘A’ is known as Antecedent.
‘B’ is known as Consequent.
A->B is real as ‘A implies B’ or ‘if A then B’ or ‘if A is to B then B is true.
[/c]

5. Tautology: Consider the following truth table:

A logical expression is a tautology that is valid. A valid expression defined as being one that is true under any interpretation.