Reasoning about Uncertainty

⊕ (in Rule of Combination), 37

⊕ (for plausibility), 54

⊕ (for expectation), 162

⊗ (for plausibility), 101

⊗ (for expectation), 162

⊥_D, 50

⊤_D, 50

~_DP, 173

~_i, 197

⊂, 15

⊆, 15

≽ (for bets), 20

≽ (on worlds), 45

≽^e, 46

, 169

, 169

, 169

, 169

≽_s, 48

≽_{w, i}, 264, 265

≽_{w, i}^e, 264

≅_i, 400

≽_i, 400

≼_i, 400

∘, 343

→, 292

⇔, 241

∧, 240

≪, 410

, 240

⇒, 241

⊨, 241

⊨^e, 264

⊨^s, 265

, 309

, 308

⊢, 249

⊢, 342

⊢_P, 294

, 42

a, 165

, 367

⊨ φ, 370

ACT_i, 208

[a, b], 15

(, μ), 378

∀xφ, 367

AX ⊢ φ, 249

α_U, 22

α₁U₁;…; α_nU_n, 105

, 151

B_i, 291

Bel, 32

_i, 261

Bel_{w, i}, 261

best_M (U), 300

best_{M, w}(U), 315

BS( ), 356

C (consequences), 164

C (common knowledge), 270

Cl(Σ), 342

Crooked, 385

D, 53

D_int, 52

D′, 99

D_lot, 383

D(μ, μ′), 108

Des_G(X), 134

D_N--structure, 398

dom (A), 367

DP, 165

, 166

DS, 164

d-sep_G(X, Y | Z), 139

E_Bel, 155

E′_Bel, 155

e_i, 273

E_μ, 150

E_μ, 159

E′_μ, 159

E_μ, 159

E′_μ, 159

E_μ|U, 176

E, 153

E, 153

E, 153

E_Pl, 154

E_{Pl, ED}, 163

E_Plaus, 155

E′_Plaus, 155

ED, 162

ED_D, 163

∃xφ, 367

, 15

_w,i, 193

H(μ), 109

I (interpreted system), 245

I(ψ₁, ψ₂ | φ), 273

I_μ(U, V | V), 125

I_Pl(U, V | V), 127

I^rv(ψ₁, ψ₂ | ψ), 273

I^rv_μ (X, Y | Z), 130

, 190

_diag, 333

K_i, 244

K ∘ φ, 343

κ, 43

KB_hep, 406

ℓ (local state), 208

ℓ_i (likelihood), 254

^≈(), 400

^→ (Φ), 311

^{→, fo}_n(), 382

^def (Φ), 292

^E_n, 273

^fo(), 367

^K_n, 244

^KQUC_n (Φ), 270

^Prop(Φ), 241

^QU_n, 255

^{QU, fo}(), 376

^{QU, stat}, 378

^QU, _n(Φ), 272

^RL_n(Φ), 264

L_i, 208

Lottery, 383

_i, 261

m, 34

M_DP, 172

M_lot, 383

M ⊨ φ 245

M ⊨ Σ, 295

_n, 250

^≈(), 400

^bel_n, 260

^cps, 295

^elt_n, 250

^et_n, 250

^{K, prob}_n, 268

^{K, meas}_n, 268

^lp_n, 260

^meas_n, 254

^meas,c_n, 260

^meas,fo_n, 376

^meas,stat_n, 378

^plaus_n, 266

^plaus,means_n, 266

^poss_n, 260

^poss,fo_n, 382

^poss+fo_n, 382

^pref_n, 264

^{pref, fo}_n, 382

^prob_n, 254

^ps, 297

^ps,fo_n, 382

^qual, 303

^qual,fo_n, 382

^r_n, 250

^rank_n, 266

^rank,fo_n, 382

^{rank+ fo}_n, 382

^rank_Φ, 307

^rank_∑, 308

^rst_n, 250

^rt_n, 250

^tot_n, 264

μ, 15

μ_*, 28

μ^*, 28

μ|α₁U₁;…; α_nU_n, 105

μ, 87

μ_∞(φ | KB), 403

μ^unif_N, 398

μ^τ_N (φ | KB), 401

μ(V | U), 74

μ_{w, i}, 193

, 17

NI_Pl(U, V | V′), 127

NonDes_G(X), 134

P_i (protocol), 208

_*, 28

*, 28

_Bel, 34

_μ, 29

, 417

_{w, i}, 261

Φ_diag, 333

Φ_diag, 333

||φ||_X, 377

Par_G(X), 134

Pl, 50

Pl_lot, 383

Pl, 52

Pl_*,*, 52

_D,⊕,⊗, 142

_i, 232, 266

Plaus, 33

Poss, 40

_i, 261

Poss_κ, 44

Poss_{w, i}, 261

, 193

π, 245

π_diag, 333

π_lot, 383

Φ, 240

Φ_e, 340

[[φ]]_M, 244

φ[x/t], 370

, 197

, 15

, 163

regret_u, 168

Rigged, 386

[], 339

[φ], 339

s_a φ, 341

, 295

st(α), 76

, 366

τ, 171, 175

, 400

u_a, 166

(U, α), 20

v, 241

V, 368

V [x/d], 368

v⊨ φ, 241

(X), 130

W, 14

W_diag, 333

W_lot, 383

, 401

, 401

worst_u, 167

W_{w, i}, 193

X^M_γ, 274

X_U, 152