Constraint inference
Encyclopedia
In constraint satisfaction
, constraint inference is a relationship between constraints and their consequences. A set of constraints
entails a constraint 
if every solution to 
is also a solution to 
. In other words, if 
is a valuation of the variables in the scopes of the constraints in 
and all constraints in 
are satisfied by 
, then 
also satisfies the constraint 
.
Some operations on constraints produce a new constraint that is a consequence of them. Constraint composition operates on a pair of binary constraints
and 
with a common variable. The composition of such two constraints is the constraint 
that is satisfied by every evaluation of the two non-shared variables for which there exists a value of the shared variable 
such that the evaluation of these three variables satisfies the two original constraints 
and 
.
Constraint projection restricts the effects of a constraint to some of its variables. Given a constraint
its projection to a subset 
of its variables is the constraint 
that is satisfied by an evaluation if this evaluation can be extended to the other variables in such a way the original constraint 
is satisfied.
Extended composition is similar in principle to composition, but allows for an arbitrary number of possibly non-binary constraints; the generated constraint is on an arbitrary subset of the variables of the original constraints. Given constraints
and a list 
of their variables, the extended composition of them is the constraint 
where an evaluation of 
satisfies this constraint if it can be extended to the other variables so that 
are all satisfied.
Constraint satisfaction
In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution to a set of constraints that impose conditions that the variables must satisfy. A solution is therefore a vector of variables that satisfies all constraints.The techniques used in...
, constraint inference is a relationship between constraints and their consequences. A set of constraints
entails a constraint if every solution to is also a solution to . In other words, if is a valuation of the variables in the scopes of the constraints in and all constraints in are satisfied by , then also satisfies the constraint .Some operations on constraints produce a new constraint that is a consequence of them. Constraint composition operates on a pair of binary constraints
and with a common variable. The composition of such two constraints is the constraint that is satisfied by every evaluation of the two non-shared variables for which there exists a value of the shared variable such that the evaluation of these three variables satisfies the two original constraints and .Constraint projection restricts the effects of a constraint to some of its variables. Given a constraint
its projection to a subset of its variables is the constraint that is satisfied by an evaluation if this evaluation can be extended to the other variables in such a way the original constraint is satisfied.Extended composition is similar in principle to composition, but allows for an arbitrary number of possibly non-binary constraints; the generated constraint is on an arbitrary subset of the variables of the original constraints. Given constraints
and a list of their variables, the extended composition of them is the constraint where an evaluation of satisfies this constraint if it can be extended to the other variables so that are all satisfied.