Safety cases play a significant role in the development of safety-critical systems. The key components in a safety case are safety arguments, that are designated to demonstrate that the system is acceptably safe. Inappropriate reasoning with safety arguments could undermine a system’s safety claims which in turn contribute to safety-related failures of the system. Currently, safety argument reviews are conducted manually, require expensive expertise and are often labour intensive. It would therefore be desirable if software can be employed to help with the detection of flaws in the arguments. A prerequisite for this approach is the need for a formal representation of safety arguments. This paper proposes a predicate logic based representation of safety arguments and a method to detect argument fallacies. It is anticipated that the work contributes to the field of the safety case development as well as to the area of computational fallacies.