Proof Theory - Kinds of Proof Calculi

Kinds of Proof Calculi

The three most well-known styles of proof calculi are:

• The Hilbert calculi
• The natural deduction calculi
• The sequent calculi

Each of these can give a complete and axiomatic formalization of propositional or predicate logic of either the classical or intuitionistic flavour, almost any modal logic, and many substructural logics, such as relevance logic or linear logic. Indeed it is unusual to find a logic that resists being represented in one of these calculi.