Question

. What are limits of propositional logic? does first order logic accomplish? Can you use examples to illustrate the limits? And what

Answer 1

Answer is as follows :

Limitations of Propositional logic :

• One key limitation is that it applies only to atomic propositions. There is no way to talk about properties that apply to categories of objects, or about relationships between those properties.
• We cannot use propositional logic to establish the truth of a proposition that isn't given as a premise means we can't represent all and some symbols in propositional logic.
• we cannot use propositional logic to reason about propositions that obey laws like arithmatic laws.

Example

Let us suppose

We have data,

All people Like Cricket than it's propositional logic is like(people, cricket).

and for

Some people Like Cricket than it's propositional logic is like(people, cricket).

Here we note that the propositional logic is same but the statements are different.

So to represent these we can't use propositional logic.

To remove these problems we use predicate logic or first order predicate logic(FOPL).

FOPL :

FOPL are used to eliminate the problems of propositional logic by using quantifiers and variables.

Two types of quatifiesrs are used in FOPL i.e. Universal Quantifier and Extential Quantifier.

Universal Quantifiers are used to represent All values.

Extential Quantifiers are used to represent Some values.

So for

example

All people like criket predicate logic is :

$\forall$ (x) likes ( cricket) where x represent peoples

and for

Some people like criket predicate logic is :

$\exists$ (x) likes(cricket).

if there is any query please ask in comments..