Fitch-style calculus

Fitch Style Calculus is a method for constructing formal proofs used in First-order logic. It was invented by American logician Frederic Brenton Fitch. Fitch-style proofs involve the atomic sentences of first order logic, which are arranged in premises, lemmas, and subproofs.

Each step in a Fitch-style proof, except premises and subproof premises, requires a citation of a rule of first-order logic in order to justify the step. After a step is justified, then another step may be constructed upon this, until a desired conclusion has been reached.

Example
Illustrated below is the simplest example of a proof known as “Reductio ad absurdum” which in Latin is “reduction to the absurd”. The argument is shown on the left, where the rules are cited on the right. [Note: Something's wrong with this example. Perhaps it is not formatted correctly; I see no citations "on the right", at least when viewed with Internet Explorer. --Mark Nowitzky, 8/5/07]


 * 1) ~P --> Q
 * 2) ~Q
 * ~P
 * 1) Q			--> Elim (1,3)
 * 2) “absurdity”		“absurdity” Intro (2,5)
 * 3) P			~ Intro (3—5)
 * 4) P			~ Elim 6

Related

 * Stanford University has produced an application called "Fitch".


 * An online Java application for proof building is also available.