Index_O-P

O-P

observation, consistent with probability measure, 106, 108, 109

one-coin problem, 3, 10, 225-226

online algorithm, 188

OR, see axioms and inference rules, OR

order, see also preorder

lexicographic, 115

partial, 45, 50, 52, 97, 99, 307, 322, 323

strict, 45

preference, 78

preference (on acts), 20-23, 166-176

ordinal numbers, 44

ordinal representation, of decision rule, see decision rule, ordinally represents another

Ostrogradsky, M. V., 66

outcomes, see possible worlds

outer expectation, see inner/outer expectation

outer measure, see inner/outer measure

P, see axiom system, P

P1–2, 15-17, 19, 40, 45, 56, 72, 75, 78

Parade Magazine, 10

parent, 133

Parikh, R. J., 235

Paris, J. B., 65, 116, 430

partial order, see preorder, partial

partial preorder, see preorder, partial

Pascal, B., 1

Patashnik, O., 430

PATHFINDER, 138, 148

PD1–5, see axioms and inference rules, PD1–5

PDGen, see axioms and inference rules, PDGen

Pearl, J., 146, 147-148, 328, 329

perfect recall, 203

Petride, S., xiv

Pfeffer, A., 394

Pl1–3, 51, 52, 53, 289, 302, 303, 304, 323, 388

Pl3′, 63

Pl4–5, Pl4′, 289-292, 299, 301-307, 313-314, 318, 319, 321-323, 326, 387, 388

Pl4*, Pl4†, Pl5*, 290, 323

Pl4*, Pl4†, Pl5*, 387-389, 392, 394

Pl6–9, 313-314, 348

Plantinga, A., 393

plausibilisticallly indistinguishable acts, see acts, plausibilistically indistinguishable

plausibilistic conditioning, see plausibility measure, conditional

plausibility assignment, 232, 319, 347

plausibility function, 33-36, 42-43, 67, 95

conditional, 92-95

plausibility measure, 4, 11, 50-54, 68, 81, 144, 208, 254, 263, 288, 289-292, 294, 301-305, 312-314, 317, 323, 326, 328, 379, 383, 387, 390, 391, 392

additive, 54, 101, 156

conditional, 97-104, 118, 126-129, 131-132

acceptable, 101

algebraic, 101, 115

expectation for, 162-164

Markovian, 232

normal, 314

rational, 314

plausibility measures

represent the same ordinal beliefs, 175

set of, 100

plausibility space, 50

conditional, 97, 113, 127, 144

acceptable, 98-104, 113

algebraic, 101-104, 113, 115, 118, 127-129, 141-143

determined by unconditional plausibility, 104

monotonic, 113

standard, 104, 128

plausibility structure, see structure, plausibility

plausibility system, 232

plausibility value, 50

point, 196, 336

probability on, see probability, on points policy, 236

Pollock, J. L., 429

polynomial likelihood formula, see likelihood formula

Poole, D., 430

Popkorn, S., 283

Popper algebra, 74, 97, 99

Popper functions, 117

Popper, K. R., 75, 117

Popper measure, 117

positive affine homogeneity, see affine homogeneity, positive

Positive Introspection Axiom, see axioms and inference rules, Positive Introspection Axiom (K4)

Poss1–3, 40-41, 60, 61

Poss3′, Poss3⁺, 40-41, 44, 60-61

possibility measure, 4, 11, 40-43, 44, 50, 51, 54, 55, 60-62, 67, 110, 115, 119, 208, 288, 298, 299, 303, 311, 312, 314, 317, 328, 376

conditional, 95-96, 102, 112, 118, 127, 129, 132, 142, 147

expectation for, 161, 186

and Jeffrey's Rule, 107

possibility measures, reasoning about, see reasoning about possibility measures

possibility relation, 190, 191, 248, 251

possibility structure, see structure, possibility

possible outcomes, see possible worlds

possible worlds, 12, 14, 17-19, 25, 55, 58, 69, 73, 82, 124, 130, 179, 212-220, 233, 248, 251, 283, 316, 317-318, 338, 374-375, 377, 378, 382, 387, 393, 395

posterior probability, 73

Prade, H., 67, 118, 147, 186, 328

preference order, see order, preference (on acts)

preferential structure, see structure, preferential

preorder, 45, see also order

partial, 45, 55, 62, 63, 264, 298, 300, 303, 312, 313, 316

qualitative probability, 68

total, 47-50, 62, 67, 267, 312, 313, 316, 329

primality testing, 226-228

primitive proposition, 240, 241

principle of indifference, 17-18, 19, 23, 64, 77, 82-83, 119

principle of insufficient reason, see principle of indifference

PRIOR, 201-205, 232

prior probability, 73

probabilistic conditioning, see probability measure, conditional

probabilistic protocol, see protocol, probabilistic

probability, 1, 3, 5, 6, 7, 14-24, 40, 43, 44, 64-65, 95, 129, 138, 249

conditional, 2, 72-81, 102, 105, 116-117, 134, 316

justification of, 77-79, 116

and default reasoning, 295-298, 302, 303-304, 305, 309-311

expectation for, 274

justification of, 18, 24, 55, 65, 186

lower, see lower/upper probability nonadditive, 68

on points, 199

reasoning about, see reasoning about probability

and relative entropy, 109

on runs, 199-205, 235, 236

updating, 108, 118

upper, see lower/upper probability

and variation distance, 108

probability assignment, 193-195, 199-202, 222-226, 232, 236, 269, 270

basic, see mass function

probability frame, see frame, probability

probability measure, 3, 14-24, 33, 36, 38, 50, 51, 54, 55, 56, 89, 94, 208

conditional, 72-77, 93, 94, 102, 110-111, 142, 143

expectation for, 150-153

Markovian, 206-207

nonstandard, 44-45, 62, 67, 76-77, 110, 119, 124, 297, 300, 321, 393

uniform, 109, 114, 378-379, 398, 416

probability measures

set of, 24-32, 34, 52-53, 55, 59, 63, 65, 129, 172

conditioning with, 81-83, 92, 93, 99-103, 113, 117, 147

expectation for, 153-160, 163, 177, 276-277

and Jeffrey's Rule, 107

probability sequence, 297-298, 304, 309-311, 314, 381, 419

probability space, 15

conditional, 75, 98, 119, 123

probability structure, see structure, probability

probability system, 199

product measure, 379

proof, 249

Prop, see axioms and inference rules, Prop

Property J, see J (Property J)

propositional attitude, 240

propositional gamble inequality, 276

propositional logic, 6, 240-243, 365, 372-373

semantics, 241-243

syntax, 366, 367

propositional modal logic, see modal logic, propositional

protocol, 6, 205, 207-217, 230, 233-234, 236

joint, 208

probabilistic, 208

provable, 249

PS structure, see structure, PS

public-key cryptography, 227

Pucella, R., xiv, 66, 284, 285

Puterman, M. L., 236

puzzle

Monty Hall, see Monty Hall puzzle

second-ace, see second-ace puzzle

three-prisoners, see three-prisoners puzzle

two-envelope, see two-envelope puzzle