Fitch notation, also known as Fitch diagrams (named after Frederic Fitch), is a notational system for constructing formal proofs used in sentential logics and predicate logics. Fitch-style proofs arrange the sequence of sentences that make up the proof into rows. A unique feature of Fitch notation is that the degree of indentation of each row conveys which assumptions are active for that step.
Each row in a Fitch-style proof is either:
Introducing a new assumption increases the level of indentation, and begins a new vertical "scope" bar that continues to indent subsequent lines until the assumption is discharged. This mechanism immediately conveys which assumptions are active for any given line in the proof, without the assumptions needing to be rewritten on every line (as with sequent-style proofs).
The following example displays the main features of Fitch notation:
0 |__ [assumption, want P if not P] 1 | |__ P [assumption, want not P] 2 | | |__ not P [assumption, for reduction] 3 | | | contradiction [contradiction introduction: 1, 2] 4 | | not not P [negation introduction: 2] | 5 | |__ not not P [assumption, want P] 6 | | P [negation elimination: 5] | 7 | P iff not not P [biconditional introduction: 1 - 4, 5 - 6]0. The null assumption, i.e., we are proving a tautology