73:
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
80:
0 |__ 1 | |__ P 2 | | |__ not P 3 | | | contradiction 4 | | not not P | 5 | |__ not not P 6 | | P | 7 | P iff not not P
50:. 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.
108:
7. From 1 to 4 we have shown if P then not not P, from 5 to 6 we have shown P if not not P; hence we are allowed to introduce the biconditional in 7, where
194:
170:
248:
161:
253:
191:
204:
A Web implementation of Fitch proof system (propositional and first-order) at proofmod.mindconnect.cc
96:
166:
124:
106:
6. We invoke the rule that allows us to remove an even number of nots from a statement prefix
89:
66:
43:
229:
FitchJS: An open source web app to construct proofs in Fitch notation (and export to LaTeX)
212:
198:
156:
47:
137:
35:
218:
242:
102:
4. We are allowed to prefix the statement that "caused" the contradiction with a not
17:
186:
39:
152:
95:
2. A subsubproof: we are free to assume what we want. Here we aim for a
104:
5. Our second subproof: we assume the r.h.s. to show the l.h.s. follows
93:
1. Our first subproof: we assume the l.h.s. to show the r.h.s. follows
233:
228:
74:
needing to be rewritten on every line (as with sequent-style proofs).
203:
77:
The following example displays the main features of Fitch notation:
69:
and (2) the prior line or lines of the proof that license that rule.
222:
219:
Resources for typesetting proofs in Fitch notation with LaTeX
234:
Natural deduction proof editor and checker in Fitch notation
208:
165:(2 ed.). CSLI Publications. p. 606.
65:a sentence justified by the citation of (1) a
192:An online Java application for proof building
8:
58:Each row in a Fitch-style proof is either:
38:), is a notational system for constructing
209:The Jape general-purpose proof assistant
62:an assumption or subproof assumption.
7:
25:
142:Symbolic Logic: An introduction
100:3. We now have a contradiction
187:Fitch's Paradox of Knowability
1:
270:
162:Language, Proof and Logic
84:0. The null assumption,
138:Fitch, Frederic Brenton
151:Barker-Plummer, Dave;
97:reductio ad absurdum
18:Fitch-style calculus
249:Philosophical logic
88:, we are proving a
197:2006-10-02 at the
144:. Ronald Press Co.
125:Natural deduction
67:rule of inference
44:sentential logics
16:(Redirected from
261:
176:
157:Etchemendy, John
145:
48:predicate logics
30:, also known as
21:
269:
268:
264:
263:
262:
260:
259:
258:
254:Logical calculi
239:
238:
199:Wayback Machine
183:
173:
150:
136:
133:
121:
107:
105:
103:
101:
99:
94:
92:
82:
56:
23:
22:
15:
12:
11:
5:
267:
265:
257:
256:
251:
241:
240:
237:
236:
231:
226:
216:
206:
201:
189:
182:
181:External links
179:
178:
177:
171:
147:
146:
132:
129:
128:
127:
120:
117:
114:if and only if
79:
71:
70:
63:
55:
52:
36:Frederic Fitch
32:Fitch diagrams
28:Fitch notation
24:
14:
13:
10:
9:
6:
4:
3:
2:
266:
255:
252:
250:
247:
246:
244:
235:
232:
230:
227:
224:
220:
217:
214:
210:
207:
205:
202:
200:
196:
193:
190:
188:
185:
184:
180:
174:
172:9781575866321
168:
164:
163:
158:
154:
149:
148:
143:
139:
135:
134:
130:
126:
123:
122:
118:
116:
115:
111:
98:
91:
87:
78:
75:
68:
64:
61:
60:
59:
53:
51:
49:
45:
41:
40:formal proofs
37:
34:(named after
33:
29:
19:
160:
153:Barwise, Jon
141:
113:
109:
85:
83:
76:
72:
57:
31:
27:
26:
112:stands for
243:Categories
131:References
159:(2011) .
90:tautology
195:Archived
140:(1952).
119:See also
42:used in
54:Example
169:
223:LaTeX
221:(see
211:(see
213:Jape
167:ISBN
86:i.e.
46:and
110:iff
245::
155:;
225:)
215:)
175:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.