Propositional Logic in Artificial Intelligence
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.
Propositions are statements used in mathematics. A proposition or sentence is classified as declarative sentence whose value is either ‘true‘ or ‘false‘.
i. The sky is blue.
ii. Snow is white
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,
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.
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.