Logic - shivamvats/notes GitHub Wiki

Propositional -> First Order -> Second Order -> Higher Order

Propositional logic consists of propositions, which are logical statements that can be either true or false. Compound propositions are formed by connecting propositions by logical connectives, like, and, or, etc. It does not deal with non-logical objects, predicates and quantifiers.

First-order logic covers everything that propositional logic deals with. It additionally covers predicates and quantification (for all, there exists).

Apart from supporting what a lower order logic supports, higher order logic additionally deals with higher order quantification, for example, second-order logic supports quantification over sets.