Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

The recognition problem is the present content needs to check the
geometric feature of the object under test and determine the object by
satisfying the premises of one of the above three constraints.
While dealing with CSP we should consider the following three issues:
i) whether the constraints are satisfiable, i.e., does the
problem has solutions that satisfy all the constraints?
ii) simplification of the constraints by equivalent simpler
ones,
iii) optimization of the solution based on some other criteria, if
more than one solution exists.
19.2 Formal Definitions
We now present a few definitions, which will be referred to throughout the
chapter.
Definition 19.1: Constraints are mathematical/ logical relationships among
the attributes of one or more objects.
To understand the above definition, let us consider the ‘make-changes of 10$’
problem, where the 1$, 2$, 5$ notes are objects and their counts are the
attributes in the problems. Thus the mathematical relationship among them is
the expression ∑ ci xi = 10$ , which is the constraint.
∃xi
Definition 19.2: The legitimate set of operators like ‘+’ , ‘* ’, ‘∧’ or ’∨’
and the type of the variables and their domains, the type of functions used
and their range and the arguments of the operators are specified by a
domain, called constraint domain.
Formally, the constraint domain D is a 5 tuple, given by
D={v, f, op, d, r}
where v denotes the set of variables,
f denotes the set of functions,
op stands for the set of legal operators to be used on variables or
functions,
d is the domain of variable, and
r is the range of the functions employed in the constraints.