What is Propotional logic| Artificial Intelligence

Propositional Logic in Artificial Intelligence

Content

1. Introduction of Propositional logic

2. Some basic facts of Propositional logic

3. Syntax of Propositional logic

      3.1 Atomic proposition 

      3.2 Compound proposition 

4. Logical operators or connectivity in Propositional logic

      4.1 Negation

       4.2 Conjuction 

       4.3 Disjunction

       4.4 Inplication

       4.5 Biconditional

1. Introduction 

   "Propositional logic in Artificial Intelligence"

                    Propositional logic  is the simplest form of logic representation and generally use in "Artificial Intelligence". Propositional logic is the simplest from of any statement in which it's ans in true Or false. It is also known as or short form is PL.
            It is the technique to represent any declaration statement or mathematical statement in the from of yes or no.It is a knowledge representative technique.

2.  Some basic facts of Propositional logic

• Propositional logic is also called the Boolean logic which does work on 0  or 1.
• Propositional logic shows the statement true or false.
• Propositional logic can not be both , either it can be true or false.
• In Propositional logic we can use the variable name like A,B,C,D,X,Y,Z ,etc
• Propositional logic consist of an object , relationship and function.            Propositional logic show there logical connectivity which is also known    as logical operators.   
• A Propositional formula which is true is called " Tautology " And the        propositional formula which is false is  known as "Contradiction".
• Statement like " Who are you? ", "where you from? ", " My name is Sunita? " Is not the type of propositional logic.

3.  Syntax of Propositional logic

If we talk in the way of syntax of propositional logic here specifically two types of propositions,

1. Atomic proposition
2. Compound proposition

• Atomic proposition

               This is the simplest proposition which always does consist  a single symbol .

Example-- The sun is too hot (true),
2×3=6(true)

• Compound proposition

              This kind of proposition always does consist two or more than two symbols .
Example --If it is raining, than there will rainbow (true).

4.  Logical connectivity or logical operator in PI

              Logical connectives are used to connect two simpler propositions or representing a sentence logically. We can create compound propositions with the help of logical connectives. There are mainly five connectives, which are given as follows:

  4.1 Negation:

                Denoted by "¬".A sentence such as (¬) P is called negation of P. A literal can be either Positive literal or negative literal.

• Truth table:   

  4.2 Conjunction:

               Denoted by "∧"A sentence which has (∧) connective such as, P ∧ Q is called a conjunction.
Example: Rohan is intelligent and hardworking.
 It can be written as like,
                A   -  Rohan is intelligent.
                B   -  Rohan is hard working.
              A^B-  Rohan  is honest and hard working.

• Truth table:

   4.3 Disjunction:

               It is denoted by "v".It simply use between two or more statement. Which work as "or"
          Example--
           A --   I will be a teacher.
           B--    I will be a doctor.
       A v B -- I will be a teacher or doctor.

• Truth table:  

   4.4 Implications --

             It is denoted by "⟶". It is also known as if, and then rule.
          Example --
           A--If Rahul will attend class .
           B--Than he will pass.
           A ⟶B

• Truth table:     

   4.5 Biconditional: 

            This Operator is denoted by "⇔".

      Example
        X -- if it will rain .
        Y --than there will be rainbow.
        X⇔Y

• Truth table:

Thank you so much ....

Prashant Rathore