Index

A

Abadi, M., 393

acceptable conditional plausibility space, see plausibility space, conditional, acceptable

accessibility relation, see possibility relation

act, 164-174, 183

simple, 165

acts

indistinguishable, 173-176

acyclic (directed graph), 132

Adams, E., 328

additive plausibility measure, see plausibility measure, additive

additivity

countable, 16, 31, 56, 59, 67, 152, 154, 378

for expectation, 151-152, 154

finite, 16, 17, 19, 90, 258, 262, 279

Adleman, L., 236

affine homogeneity, 151-152, 154

positive, 153-161, 180

AGM postulates, see R1–8

AGM revision, see R1–8

Agrawal, M., 236

Alchourr n, C. E., 342, 363

Alg1–4, Alg4′, 101-104, 113, 128, 132

algebra, 15, 27-31, 32, 50, 55, 57, 74, 89, 206, 223, 233

Popper, see Popper algebra

σ-, 15, 16

algebraic conditional plausibility measure, see plausibility measure, conditional, algebraic

algebraic conditional plausibility space, see plausibility space, conditional, algebraic

Allais, M., 186

ancestor, 133

AND, see axioms and inference rules, AND

Anderson, A., 283

Anger, B., 66

antisymmetric relation, 45

approximate equality, 397, 399-402, 404, 411, 417, 419-420, 423-428, 429, 430

arity, 366

Artzenius, F., 188

Ash, R. B., 64

assignment to variables, 259

asynchronous system, 205

atom, 324, 417-418

atomic formula, see formula, atomic Aumann, R. J., 235

Aumann structure, see structure, Aumann

autoepistemic logic, 328

AX^bel_n, see axiom system, AX^bel_n

AX^cond, see axiom system, AX^cond

AX^cond, see axiom system, AX^{cond, fo}

axioms and inference rules, 239, 249-251, 253

AND, 293, 296, 297, 298, 299, 300, 302-303, 313, 321, 322, 413

C1–8, 312-317, 327, 383, 386, 394, 426 C9–11, 386-389, 392, 394

CM, 293-294, 296, 297, 298, 300, 302, 303, 313, 321, 322, 325, 413

for conditional independence, 146

Consistency Axiom (K3), 249, 250

for counterfactuals, 316-317, 329

CP₂, 270-271, 281-282, 285

CUT, 310, 325, 415, 426

Distribution Axiom (K1), 246, 248, 249, 250

EV, 380, 391

EXP1–11, 276-278

F1–5, 370, 375-376, 380, 381, 391, 394

FIN_N, 371, 391

for first-order logic, see first-order logic, axioms

for first-order modal logic, see modal logic, first-order, axioms

induction axiom, 373

Ineq, 258-259, 276, 284

Ineq⁺, 272

IV, 380, 382, 391

IVPl, 382, 391

K1–5, 370, 375

for knowledge and belief, 291-292, 320

for knowledge and probability, 268-271

Knowledge Axiom (K2), 247, 249, 250, 268

KP1–3, 269-270, 281

LLE, 293, 296, 297, 298, 302, 303, 313, 321, 345, 413

Modus Ponens (MP), 250

Negative Introspection Axiom (K5), 247, 250

OR, 293, 296, 297, 298, 300, 302, 303, 313, 321, 322, 413, 414

PD1–5, 380-381

PDGen, 381

Positive Introspection Axiom (K4), 246, 250

Prop, 249, 250, 258, 265, 276

QU1–8, 258-263, 277, 380

QUGen, 258

for rationality, see RAT1–4, RAT5

RC1–2, 312

REF, 293, 294, 296, 297, 298, 302, 313, 321, 413

RL1–6, 265-266, 267

Rule of Knowledge Generalization (Gen), 246, 248, 250, 265

RW, 293, 296, 297, 298, 302, 303, 313, 321, 413

UGen, 370, 391, 394

axiom system, 249

AX^bel_n, 262, 279, 280

AX^cond, 312-314, 316, 326, 327, 329, 381, 382, 426

AX^{cond, fo}, 382-386

AX^fo, 370-372, 391

AX^fo_N, 371

AX^lp_n, 263

AX^ord_n, 266-267

AX^poss_n, 262

AX^prob_n, 258-260, 279

AX^{prob, fo}_{n, N}, 380

AX^prob, _n, 272

AX^RLe, 265-267

AX^RLs, 265-267

AX^RLTe, 265-267

AX^RLTs, 265-267, 280-281

AX^stat_N, 380-381

K, 250, 283

K_n, 251

K45_n, 251

KD45, 250

KD45_n, 250, 251

KT4, 250

P, 293-311, 313, 320, 321, 323, 324, 325, 328, 329, 345, 354-355, 413-415, 419, 426

for propositional logic, 283

S4, 250, 283

S4_n, 251

S5, 250, 283

S5_n, 250, 251

sound and complete, 249

T, 250, 283

T_n, 251

AX^ord_n, see axiom system, AX^ord_n

AX^poss_n, see axiom system, AX^poss_n

AX^prob_n, see axiom system, AX^prob_n

AX^{prob, fo}_{n, N}, see axiom system, AX^{prob, fo}_{n, N}

AX^prob, _n, see axiom system, AX^prob, _n

AX^stat_N, see axiom system, AX^stat_N

AX^RLe, see axiom system, AX^RLe

AX^RLs, see axiom system, AX^RLs