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:
“...you are like whitewashed tombs, which on the outside look beautiful, but inside they are full of the bones of the dead and of all kinds of filth.”
—Bible: New Testament, Matthew 23:27.
“There are two kinds of adventurers: those who go truly hoping to find adventure and those who go secretly hoping they won’t.”
—William Least Heat Moon [William Trogdon] (b. 1939)
“If some books are deemed most baneful and their sale forbid, how, then, with deadlier facts, not dreams of doting men? Those whom books will hurt will not be proof against events. Events, not books, should be forbid.”
—Herman Melville (1819–1891)