Testing Conceptual Schema Satisfiability - Intentional Perspectives on Information Systems Engineering - page 278

3.1 Base Type Satisfiability

Satisfiability (or liveliness) is a well known property of base entity and relationship
types. A base type is satisfiable (or lively) if it may have a non empty finite popu-
lation at certain time. In a conceptual schema, a base type is unsatisfiable when the
set of constraints defined in that schema can only be satisfied if the population of
that type is empty or infinite [ 17] . In conceptual modeling, it is usually required that
all base types be satisfiable [4, 6, 14] .
Let T i be a base type (entity types, attributes and associations) defined in a con-
ceptual schema. The satisfiability of T i can be checked by means of testing. The idea
is to set up a test case TC j such that it:

• builds a state of the IB having at least one instance of T i , and

• makes an assertion TA k that can only Pass if the above IB state is consistent (that

is, it satisfies all constraints).

If the execution of TA k gives the verdict Pass , then it is experimentally proved
that T i is satisfiable. Note that in a single test case we can instantiate several types
and that a single assertion can experimentally prove that all of them are satisfiable.
In the test program of Fig. 3, the fixture creates the customer john and the
session s . It also initializes the online catalog with the product shirt and the special
product trousers . The execution of any of the test cases of the test program exam-
ple implies the execution of this fixture and ensures that the entity types Customer ,
Session , Product and Special (and also their attributes) are satisfiable.
Moreover, the test case confirmOrder adds a shopping cart item with two
units of shirt and another item with a pair of trousers . The shopping cart is
created when adding the first item. By this way, the entity types ShoppingCart
and ShoppingCartItem (and also their relationship types, including attributes)
are proved satisfiable. The relationship types ShoppingCart-Session, Session-
Customer and Customer-ShoppingCart are also satisfiable when the LogIn event
occurs (the session is assigned to a customer and the anonymous shopping cart
becomes the shopping cart of the customer of the session). The entity types
Order and OrderLine (and their relationship types) become satisfiable when the
event OrderConfirmation occurs (the order and its order lines are created from
the shopping cart). Finally, the occurrence of the instance ndp of the domain
event type NewDownloadableProduct proves the satisfiability of the entity type
DownloadableProduct .
If a conceptual schema includes a base type T i that is unsatisfiable, then the
conceptual modeler will be unable to set up a test case that builds a state of the IB
with at least one instance of T i , and an assertion that can only Pass if that state is
consistent. This is not formal proof that T i is unsatisfiable, but in many practical
cases it provides a clue that helps to uncover a faulty constraint.
For example, consider the schema example shown in Fig. 4 (adapted from [4] ).
The association Manages is satisfiable if we do not take into account that Manager