INDEX

adaptive consistency, see bucket elimination

addition-is-max semiring

adjacency matrix

affine space

algebraic information theory

algebraic path problem

all-pairs problem

multiple-pairs problem

simple path

single-pair problem

single-source problem

single-target problem

AND-OR search

arithmetic potential

assumption-based constraint

assumption-based reasoning

in constraint systems

in Gaussian systems

attribute, see variable

backward substitution

basic probability assignment, see mass function

Bayesian decoding

Bayesian network

construction order

posterior probability

query and evidence variable

query event

belief function

Bellman-Ford algorithm

Bellmann’s principle of optimality

Boolean function, see indicator function

bucket elimination

bucket-tree

bucket-tree elimination

Choleski decomposition

chordal graph, see triangulated graph

clique

maximal

closed set

closure operator

cluster tree elimination, see -Shafer architecture

collect algorithm

combination

combination axiom

commonality function

communication channel

computational graph

concentration matrix

configuration, see tuple

configuration extension set

for optimization problem

for quasi-regular valuation algebra

for symmetric, positive definite system

congruence relation

connectivity problem

consequence finding

consequence operator

constraint formalism

constraint problem

constraint semiring, see c-semiring

context

context valuation algebra

control of fill-ins

convex polyhedra

convolutional code

counter-model

covering join tree

for factorization

for inference problem

free variable

valuation assignment

crisp constraint, see indicator function

Dempster rule

Dempster-Shafer theory of evidence

density function

conditional

support

Dijkstra algorithm

dioid

topological

disbelief function

discrete cosine transform

discrete Fourier transform

amplitude

time and frequency domain

distance tree

distributive law

domain

domain axiom

domain-free valuation algebra

support

dual graph

dynamic programming

eliminator

equivalence relation

existential quantifier

factor graph, see valuation network

factorization vs. decomposition

family of compatible frames

fast Fourier transform

fast Hadamard transform

fiducial distribution

fill-in

focal set

focal space

focusing, see projection

frame

variable

variable set

frame of discernment

fusion algorithm

graphical representation

fuzzy set, see probabilistic constraint

Gallager–Tanner–Wiberg algorithm

Galois connection

Galois field

Gauss-Jordan method

Gaussian Bayesian network

construction sequence

observation

Gaussian density

concentration matrix

conditional

head and tail

expected value

mean vector

variance-covariance matrix

Gaussian diagnostic estimation

Gaussian distribution, see Gaussian density

Gaussian dynamic system

filtering, smoothing and projection problem

Gaussian hint

precise, see Gaussian hint

Gaussian information

Gaussian potential

Gaussian predictive estimation

Gaussian variable elimination

pivoting

generalized collect algorithm

generalized Gaussian potential

generalized relational algebra

generic

generic construction

generic inference

graph

bipartite

connected

cut node

cycle

degree

directed

directed, weighted

edge and node

labeled

labeling function

neighboring node

ordered, see ordered graph

path

length

source and terminal node

triangulated

undirected

greatest lower bound, see infimum

Green relation

group

Hadamard transform

Hamacher product

hidden Markov chain

filtering, prediction, smoothing

hint, see Gaussian hint

HUGIN architecture

hybrid inference methods

hypergraph

hyperedge

hypothesis

idempotent architecture

implicate

prime

indicator function

inference

exact and approximated

inference problem

induced width

multi-query

separator width

single-query

treewidth, see treewidth

infimum

infomorphism

information algebra

information set

theory

Jacobi matrix

join graph

join tree

binary

directed

parent, child and leaf

node domain

node factor

join tree factorization

join tree property, see running intersection property

joint probability distribution

joint valuation, see objective function

junction tree, see join tree

Kalman filter

filter problem

gain matrix

one-step forward prediction

Kleene algebra

Kleene valuation algebra

knowledge compilation

knowledgebase

inconsistent

labeled matrix

direct sum

domain

extension

identity

projection

zero element

labeling

labeling axiom

language of an automaton

lattice

bottom and top element

bounded

complete

conditional independence

distributive

independence

Lauritzen-Spiegelhalter architecture

LDR-decomposition

least probable configuration

least squares method

least squares estimate

normal equation

least upper bound, see supremum

Lindenbaum algebra

linear codes

linear dynamic system

filter solution

one-step predictor

smoothing solution

with Gaussian disturbances, see Gaussian dynamic system

linear equation system

equivalence

minimal system

solution space

linear functional model

linear inequality

linear mapping

null space

range

rank

linear programming

linear space

dimension

local computation

LV-decomposition

mailbox

marginal problem

marginal set

marginalization, see projection

Markov chain

transient and recurrent state

transition matrix

Markov property, see running intersection property

Markov state evolution model

Markov tree, see join tree

mass function

matrix compilation

matrix power sequence

maximum capacity problem

maximum likelihood decoding

maximum reliability problem

maximum satisfiability problem

monoid

most probable configuration

multigraph

natural join

network compilation

neutrality axiom

nil-potent maximum t-norm

nullity axiom

numeric partial differentiation

objective function

optimization problem

configuration extension

solution configuration

OR search with caching

order of information

order relation

ordered graph

induced graph

induced width

node width

width

parameterized complexity

parity check matrix

partial k-tree, see treewidth

partial order

partition

block

partition lattice

decomposition mapping

path counting problem

possibilistic constraint

possibility measure

possibility potential

powerset

predecessor matrix

predicate logic

rank of predicate

preorder

primal graph

principal ideal

probabilistic constraint

probabilistic semiring

probability potential

projection

projection axiom

projection problem, see inference problem proposition

valuation

propositional formula

atomic

equivalence

interpretation

model

satisfiable

valuation

propositional information

propositional logic

clause

conjunctive normal form

context

literal

normal forms

resolution

resolvant

subsumption

propositional theory

pseudo-concentration matrix

quasi-inverse

quasi-regular valuation algebra

query

quotient algebra

refinement mapping

regular algebra

relation

relational algebra

selection operator

relational representation

resolution algorithm

ring

of polynomials

running intersection property

satisfiability

in constraint system

in propositional logic

satisfiability problem, see satisfiability

scaled HUGIN architecture

scaled Lauritzen-Spiegelhalter architecture

scaled Shenoy-Shafer architecture

scaled valuation algebra

search methods

semi-join

semigroup

cancellative

commutative

regular

separative

semigroup axiom

semilattice

semiring

bounded

c-semiring

cancellative

commutative

idempotent

multidimensional

of matrices

positive

quasi-regular

regular

separative

unit and zero element

semiring fixpoint equation

semiring matrix

power sequence

semiring valuation algebra

sensor network

separator

width

set potential

support

set-based constraint

set-based semiring valuation algebra

Shenoy-Shafer architecture

collect or inward phase

distribute or outward phase

shortest distance problem

shortest distance tree

simple semiring, see bounded semiring

singleton

solution configuration

solution set

in optimization problem

in quasi-regular valuation algebra

in symmetric, positive define system

space-for-time trade

sparse matrix

sparse matrix techniques

Spohn potential, see weighted constraint

stability axiom

subset lattice, see powerset

sup-topology

convergence

limit

super-bucket scheme

super-cluster scheme, see super-bucket scheme

support

supremum

Sylvester construction

symmetric, positive definite system

non-zero structure

t-conorm

t-norm, see triangular norm

tabular representation, see relational representation

time-discrete, linear dynamic system, see linear dynamic system

time-for-space trade

transitivity axiom

tree

directed

root node

undirected, see tree

tree of diagnoses

tree-decomposition, see covering join tree

treewidth

triangular norm

triangulation

tuple

domain

extension and projection

tuple set, see relation

tuple system

turbo code

uninorm

updating methods

consistent update

vacuous extension

valuation algebra

cancellative

conditional

consistent

division

idempotent

identity element

instance

inverse element

neutral element

null element

ordered

partial projection

regular

scaled or normalized

separative

stable

transport

weight predictable

valuation network

variable

binary

Boolean, see propositional variable

propositional

variable elimination operator

variable elimination sequence

induced width

variable-valuation-linked-list

vector, see tuple

Walsh function

Warshall-Floyd-Kleene algorithm

weight function

weight predictor

weighted constraint

zero-pattern