Difference between Propositional Logic and Predicate Logic

Propositional Logic

Propositional logic consists of a declarative statement with a truth value, i.e., true or false, and can never be both simultaneously. In proposition logic, we generally analyze the proportions/statements. 

For example:

• It is sunny
• 3+2=5
   

The above statements can be true or false.

The statements are represented using symbols. The propositions are combined using symbols known as logical connectives. Below are some of the most commonly used logical connectives:

• AND (∧)
• OR (∨)
• NOT (¬)
• IF AND ONLY IF (↔)
• IF….THEN ( →)
   

For example, if A is the proposition that says, “It is sunny”, and B proposition says, “Ninja will go outside”, then A→B represents, “If it is sunny, then Ninja will go outside”.

Recommended read- Propositions And Compound Statements

Predicate Logic

Predicate logic consists of a predicate that gives further information about a sentence’s subject. It can be referred to as an attribute that determines the properties of the subject in a sentence. Variables represent a subject, and then the predicate is applied to the variables.

For example, Predicate: A(Ninja1): “Ninja1 has 5 extra skills”.

In the example above, ‘Ninja1’ is the subject, while ‘has 5 extra skills’ gives additional knowledge about the subject. We can also assign some specific value to a variable, such as, ‘5 is greater than 3’. Here, 5 is the subject (with some specific value).

Domain of Discourse 

The ‘Universe/ Domain of discourse/ Domain of Predicate’ are the values from which we can assume the variables. 

Example

While considering whole numbers, the ‘domain of discourse’ consists of values {0,1,2,3,...}; therefore, the variable’s value should be among these sets of values. 

Difference between Propositional Logic and Predicate Logic

Also see, AMD vs Intel

Frequently Asked Questions

What is Prepositional Logic?

Propositional logic consists of a declarative statement with a truth value i.e., true or false, and can never be both simultaneously. In proposition logic, we generally analyze the proportions/statements. The statements are represented using symbols. 

What is Predicate Logic?

Predicate logic consists of a predicate that gives further information about a sentence’s subject. It can be referred to as an attribute that determines the properties of the subject in a sentence. 

What is the difference between Prepositional logic and Predicate logic?

Propositional logic consists of a declarative statement with a truth value, i.e., true or false. Predicate logic consists of a predicate that gives further information about a sentence’s subject. 

Why is Propositional logic used?

Propositional logic is used for analyisng simple logical connections. Predicate logic is used for expressing complex connections ad decisions for a given variable.

What is the Domain Of Discourse?

The ‘Domain of disclosure’ are the values from which we can assume the variables. Variables represent a subject, and then the predicate is applied to the variables.

Conclusion 

In this article, we have learned the difference between propositional logic and predicate logic. To level up your understanding of propositional and predicate logic and to practice questions refer to the following articles.
 

• Propositional and First Order Logic (Part-1)
• Propositional and First Order Logic (Part-2)
• Propositional and First Order Logic (Part-3)

You can read more such descriptive articles on our platform, Coding Ninjas Studio. You will find straightforward explanations of almost every topic on the platform. So take your coding journey to the next level using Coding Ninjas.
 

Happy coding!