- Aegis
- Aristotle
- Axioms
- Begriffsschrift
- Bunched implication
- Calculus of structures
- Charles Sanders Peirce
- Cirquent calculus
- Consequence relation
- Deep inference
- Design pattern
- Display logic
- Existential graph
- First-order logic
- Formal language
- Formal proof
- Formulae-as-types correspondence
- Functional programming
- Gerhard Gentzen
- Gottlob Frege
- Hilbert system
- Hilbert-Ackermann system
- Hypersequent
- Intuitionistic logic
- Mathematical logic
- Method of analytic tableaux
- Natural deduction
- Organon
- Proof net
- Propositional logic
- Propositional proof system
- Quantifier (logic)
- Relevance logic
- Resolution (logic)
- Rules of inference
- Sequent calculus
- Statement (logic)
- Structural proof theory
- Syllogistic
- Term logic
- Theorem
- Well-formed formula