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.
Read more about this topic: Proof Theory
Famous quotes containing the words kinds of, kinds and/or proof:
“I have three kinds of friends: those who love me, those who pay no attention to me, and those who detest me.”
—Sébastien-Roch Nicolas De Chamfort (1741–1794)
“There are two kinds of people one can call reasonable: those who serve God with all their heart because they know him, and those who seek him with all their heart because they do not know him.”
—Blaise Pascal (1623–1662)
“a meek humble Man of modest sense,
Who preaching peace does practice continence;
Whose pious life’s a proof he does believe,
Mysterious truths, which no Man can conceive.”
—John Wilmot, 2d Earl Of Rochester (1647–1680)