Software test data adequacy criteria are rules to determine whether a
piece of software has been adequately tested. Since Goodenough and Ger
hard pointed out that the central problem of software testing is 'what
is a test data adequacy criterion', many test data adequacy criteria
have been proposed and investigated in the literature. Each criterion
has its own strength and weakness. The comparison of these adequacy cr
iteria has long been desirable but unsatisfactory, One of the approach
es to compare existing software test adequacy criteria is to assess th
em against our intuitive concept of software test adequacy, by present
ing a set of axioms of the ideal test adequacy criterion and checking
if existing criteria satisfy these axioms. Weyuker is perhaps the firs
t computer scientist who explicitly employs the notion of axiom system
s in the study of software testing, However, an open problem in the ap
plication of this approach is how to avoid the weakness in the use of
negative properties as axioms. In the study of control flow graphs, Ba
ker et al. have proposed five properties as the requirements of contro
l flow-based adequacy criteria. These properties are positive requirem
ents of test adequacy criteria, but informal and less systematic, Some
of the properties conflict with Weyuker's axioms. In the paper, we pr
opose an axiom system combining the framework of Weyuker's system with
Baker et al's positive properties. These properties are analysed, for
malised and modified. A set of control flow-based test adequacy criter
ia is assessed against these axioms.