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Deep inference

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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.
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Deep inference is not important in logic outside of structural proof theory, since the phenomena that lead to the proposal of
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was developed as a system of deep inference allowing to explicitly account for the possibility of subcomponent-sharing.
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to permit inference to occur in contexts of high structural complexity. The term
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in an attempt to characterise the essence of structural proof theory. The
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where the structural complexity is unbounded; in this article we will use
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Intro and reference web page about ongoing research in deep inference.
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Kai Brünnler, "Deep Inference and Symmetry in Classical Proofs" (
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was proposed in order to give a cut-free characterisation of
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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:.

Index

help improve it
make it understandable to non-experts
Learn how and when to remove this message
mathematical logic
structural proof theory
sequent calculus
structure
proof calculi
formal systems
cut-elimination theorem
Kurt Schütte
Nuel Belnap
display logic
calculus of structures
noncommutative logic
Cirquent calculus
Ph.D. thesis 2004
ISBN
978-3-8325-0448-9
Deep Inference and the Calculus of Structures
Stub icon
logic
stub
expanding it
v
t
e
Categories
Proof theory
Inference

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