Since formal specifications precisely describe the software requirements in a form that can be automatically manipulated, they can be used as the base for automatic test generation and software verification. Logic coverage criteria are the common criteria used in specification-based testing. The main problem of applying these criteria that test engineers face is how to appropriately select each criterion. Thus, the comparison and analysis of these criteria will give a guide to applying each criterion. Axiomatic assessment of test adequacy criteria is an approach to comparing test criteria. This approach defines the intuitive requirements of ideal test adequacy criteria as some axioms, then compares the test adequacy criteria by checking if they satisfy these axioms. This paper proposes some positive properties as the intuitive requirements of ideal logic coverage criteria, and gives a generating algorithm that is used to determine whether a logic coverage criterion is complete. These properties are formally defined as an axioms system. With these formal definitions, the relations among the logic coverage criteria are described as some theorems. Finally, the common logic coverage criteria are assessed against the axioms system. From the assessing result, testers can get some conclusions that help them apply these criteria in practice.