Systems of Logic

Propositional logic and predicate logic are two different systems of logic that are used to represent and analyze the structure of arguments. Here’s a brief overview of the differences:

Propositional Logic:
Deals with propositions, which are statements that can be either true or false.
Analyzes the logical operators and the structure of compound statements built from these propositions.
Does not consider the internal structure of propositions; it treats them as atomic units.
Uses logical connectives like AND ( ∧ ), OR ( ∨ ), NOT ( ¬ ), IF…THEN ( → ), and IF AND ONLY IF ( :left_right_arrow: ).

Predicate Logic:
Extends propositional logic by dealing with predicates, which are functions that can be applied to objects in a domain of discourse.
Considers the internal structure of propositions, allowing for a more detailed analysis of arguments.
Includes quantifiers like the universal quantifier ( ∀ ) and the existential quantifier ( ∃ ), which allow for statements about ‘all’ or ‘some’ objects within a domain.
Allows for a more expressive language to discuss properties of objects and relationships between them.

In essence, propositional logic is concerned with the truth values of statements without regard to their content, while predicate logic can express and reason about the properties of objects and the relationships between them. Predicate logic is more powerful and expressive, capable of representing more complex statements about the world.