200:
22:
40:
103:
to refer to calculi that have structural complexity greater than the sequent calculus, but not unboundedly so, although this is not at present established terminology.
178:
241:
58:
106:
Deep inference is not important in logic outside of structural proof theory, since the phenomena that lead to the proposal of
140:
was developed as a system of deep inference allowing to explicitly account for the possibility of subcomponent-sharing.
234:
111:
80:
129:
260:
270:
133:
227:
265:
88:
72:
174:
137:
211:
84:
115:
254:
125:
107:
96:
184:
91:
to permit inference to occur in contexts of high structural complexity. The term
121:
170:
128:
in an attempt to characterise the essence of structural proof theory. The
199:
99:
where the structural complexity is unbounded; in this article we will use
187:
Intro and reference web page about ongoing research in deep inference.
207:
169:
Kai Brünnler, "Deep
Inference and Symmetry in Classical Proofs" (
15:
132:
was proposed in order to give a cut-free characterisation of
118:, but the idea did not generate much interest at the time.
114:. The first calculus of deep inference was proposed by
215:
36:
31:
may be too technical for most readers to understand
156:Kurt Schütte. Proof Theory. Springer-Verlag, 1977.
173:), also published in book form by Logos Verlag (
235:
185:Deep Inference and the Calculus of Structures
8:
110:with deep inference are all related to the
242:
228:
59:Learn how and when to remove this message
43:, without removing the technical details.
149:
41:make it understandable to non-experts
7:
196:
194:
214:. You can help Knowledge (XXG) by
14:
198:
20:
83:that breaks with the classical
87:by generalising the notion of
1:
287:
193:
95:is generally reserved for
79:names a general idea in
112:cut-elimination theorem
81:structural proof theory
210:-related article is a
130:calculus of structures
101:non-shallow inference
134:noncommutative logic
73:mathematical logic
223:
222:
179:978-3-8325-0448-9
171:Ph.D. thesis 2004
138:Cirquent calculus
69:
68:
61:
278:
244:
237:
230:
202:
195:
157:
154:
85:sequent calculus
64:
57:
53:
50:
44:
24:
23:
16:
286:
285:
281:
280:
279:
277:
276:
275:
251:
250:
249:
248:
191:
166:
164:Further reading
161:
160:
155:
151:
146:
65:
54:
48:
45:
37:help improve it
34:
25:
21:
12:
11:
5:
284:
282:
274:
273:
268:
263:
253:
252:
247:
246:
239:
232:
224:
221:
220:
203:
189:
188:
182:
165:
162:
159:
158:
148:
147:
145:
142:
108:formal systems
93:deep inference
77:deep inference
67:
66:
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
283:
272:
269:
267:
264:
262:
259:
258:
256:
245:
240:
238:
233:
231:
226:
225:
219:
217:
213:
209:
204:
201:
197:
192:
186:
183:
180:
176:
172:
168:
167:
163:
153:
150:
143:
141:
139:
135:
131:
127:
126:display logic
123:
119:
117:
113:
109:
104:
102:
98:
97:proof calculi
94:
90:
86:
82:
78:
74:
63:
60:
52:
42:
38:
32:
29:This article
27:
18:
17:
261:Proof theory
216:expanding it
205:
190:
152:
120:
116:Kurt Schütte
105:
100:
92:
76:
70:
55:
46:
30:
271:Logic stubs
122:Nuel Belnap
49:August 2022
255:Categories
266:Inference
124:proposed
89:structure
35:Please
177:
208:logic
206:This
144:Notes
212:stub
175:ISBN
71:In
39:to
257::
181:).
136:.
75:,
243:e
236:t
229:v
218:.
62:)
56:(
51:)
47:(
33:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.