Sentential Probability Logic: Origins, Development, Current Status, and Technical Applications

Title ......Page 1
Copyright ......Page 2
Contents ......Page 3
Preface ......Page 5
Introduction ......Page 9
0.1 Verity sentential logic ......Page 20
0.2 Indefinite descriptions ......Page 25
0.3 Unspecified truth values. Don\'t-care logic ......Page 30
0.4 Don\'t-care conditions in logic design ......Page 35
0.5 Elimination. Linear programming ......Page 39
1.1 Leibniz\'s vision ......Page 47
1.2 Jakob Bernoulli — probability logic via the fates of gamblers ......Page 49
1.3 Degree of certainty of an argument ......Page 54
1.4 On combining two or more arguments ......Page 58
1.5 J. H. Lambert — probabilistic syllogisms ......Page 65
1.6 Bayes — and a problem \"... no less important than curious\" ......Page 74
1.7 John Michell on the distribution of the fixed stars ......Page 78
2.1 Probability in Bolzano\'s Wissenschaftslehre 1831 ......Page 82
2.2 De Morgan — testimony and argument ......Page 89
2.3 Probable inference via six problems ......Page 96
2.4 George Boole — claims for a general method ......Page 105
2.5 Examination of Boole\'s general method ......Page 110
2.6 On combining \'evidence\' ......Page 119
2.7 Peirce and MacColl — conditional probability symbolized ......Page 126
3.1 Confirmation from Keynes to Carnap ......Page 133
3.2 Reichenbach: probability as multi-valued logic ......Page 141
3.3 Probabilistic inference revived ......Page 146
3.4 Bounds on probability — early history ......Page 150
3.5 Best possible probability bounds ......Page 160
3.6 Transmission of uncertainties in inferences ......Page 166
3.7 Nilsson\'s probabilistic logic ......Page 173
3.8 Probability logic of Scott and Krauss (1966) ......Page 180
4.1 What is a logic? ......Page 185
4.2 Probability functions on sentential languages ......Page 186
4.3 Probability logic: the finite case ......Page 189
4.4 Probability logic: the potential infinite case ......Page 192
4.5 Interval probability logic ......Page 197
4.6 Decision procedure for interval logic ......Page 204
4.7 Set-theoretic versus logic-theoretic probability ......Page 208
5.1 Conjunction and the multiplication of probabilities ......Page 211
5.2 Independence: logical and stochastic ......Page 216
5.3 Logical consequence with probability conditionals ......Page 222
5.4 Logical consequence featuring intervals ......Page 227
5.5 Boole\'s challenge problem ......Page 239
5.6 Suppositional logic ......Page 244
5.7 Probability on conditional events ......Page 251
5.8 Other writers on conditional events ......Page 256
6.1 A theorem of Renyi\'s and extensions ......Page 265
6.2 Linear programming in probability/statistics ......Page 268
6.3 Circuit fault testing. Fault trees ......Page 274
6.4 Network reliability ......Page 279
Bibliography ......Page 286
Index ......Page 299