Unary Constraint - restricts the value of a single variable
Binary Constraint - restricts the values of two variables through a relation
Global Constraint - constraint involving an arbitrary number of variables

node-consistency (1-consistency)

The node representing a variable V in constraint graph is node consistent if for every value x in the current domain of V, each unary constraint on V is satisfied

arc-consistency (2-consistency)

Arc (V_i,V_j) is arc consistent if for every value x the current domain of V_i there is some value y in the domain of V_j such that V_i=x and V_j=y is permitted by the binary constraint between V_i and V_j

(exp. this constraint graph is arc consistent but there is no solution that satisfies all the constraints)

path-consistency v 3-consistency

3-consistency coincides with path consistency only if all constraints are binary, because path consistency does not involve ternary constraints while 3-consistency does

k-consistency

A graph is k-consistent if, for any set of k-1 variables and for any consistent assignment to those variables, a consistent value can always be assigned to any k^th variable

strongly k-consistent

A graph is strongly k-consistent If it is k-consistent and is also (k-1) consistent, (k-2) consistent… all the way down to 1

bounds consistency

The node representing a variable V_i in constraint graph is bound consistent if both the lower-bound and upper-bound values of domain of V_i, there exists some value of V_jthat satisfies the constraint between V_iand V_jfor every variable V_j

directional arc and path consistency

Assuming that the order of evaluation of the variables is , a constraint satisfaction problem is directionally arc consistent if every variable is arc consistent with any other variable such that . Directional path consistency is similar, but two variables have to be path consistent with only if .