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The introduction of safety cases into the practice of safety assurance has revolutionized safety engineering. Via a 'safety argument', a safety case aims to explicate, and to provide some structure for, the kind of reasoning involved in demonstrating that a system is safe. To date, there are several notations for writing down safety arguments. These notations suffer from not having a well-founded semantics, making them deficient w.r.t. the requirements of a serious approach to engineering. We consider that a well-founded semantics for safety arguments ought to be based on logical principles in the form of a logical calculus. Logic is the basis for reasoning in mathematics, philosophy, and science, and the same should be true for safety reasoning. With this goal in mind, we take some steps towards constructing a logical calculus for safety arguments by exploring some of the features of this calculus. Moreover, we look into the essential role that evidence plays in safety arguments. Evidence sets apart safety arguments from their traditional logical counterpart, as assumptions in safety arguments must be grounded on (i.e., justified by) data from the empirical world. We present our thoughts on these matters, and illustrate them by means of examples. We consider that our work establishes a framework for discussing safety arguments in a more rigorous manner.

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Incremental design is an essential part of engineering. Without it, engineering would not likely be an economic, nor an effective, aid to economic progress. Further, engineering relies on this view of incrementality to retain the reliability attributes of the engineering method. When considering the assurance of safety for such artifacts, it is not surprising that the same economic and reliability arguments are deployed to justify an incremental approach to safety assurance. In a sense, it is possible to argue that, with engineering artifacts becoming more and more complex, it would be economically disastrous to not "do" safety incrementally. Indeed, many enterprises use such an incremental approach, reusing safety artifacts when assuring incremental design changes. In this work, we make some observations about the inadequacy of this trend and suggest that safety practices must be rethought if incremental safety approaches are ever going to be fit for purpose. We present some examples to justify our position and comment on what a more adequate approach to incremental safety assurance may look like.