Understanding the Logic of System Testing

This article discusses the logic of system testing and how to construct the valid proofs that testers can use to assess the quality of a software product.

Test case is a fundamental term used by all software testers. Numerous published sources, including the Institute of Electrical and Electronics Engineers (IEEE) Standard 610 (IEEE Std. 610), define what a test case is, techniques to design test cases, and templates to document them. However, testers in the field still find these definitions confusing, and they frequently mean different things when referring to test cases.

A common misunderstanding of test cases can be a symptom of a larger issue–a misunderstanding of the logic of software testing. The main purpose of software testing can be defined as exploring the software product to derive and report valid conclusions about its quality and suitability for use. In this regard, software testing is similar to mathematics–they both need proofs for their conclusions. However, mathematicians surpass software testers in deriving and proving their conclusions thanks to their skill in using a powerful tool called deductive reasoning . To construct valid arguments, logicians have developed proof strategies and techniques based on the concepts of symbolic logic and proof theory [1, 2, 3].

On critical software projects, testers have always been required to present valid evidence supporting their conclusions about the product's quality. The recent Sarbanes-Oxley Act1 makes this requirement much more important going forward. In this article, I discuss the logic of one of the conventional levels of testing –system test [4]–and propose a formal approach to constructing valid arguments supporting testers' conclusions. Finally, understanding the system test logic can help testers better understand the meaning of test cases.

Proofs and Software Testing
Software testers have always dealt with proofs on their projects. One example can be concluding that a system passed testing. As testers can never prove the absence of bugs in a software product, their claim that a system passed testing is conditional upon the evidence and arguments supporting such a claim. On critical projects, either the project's manager, end-users, or a compliance department commonly require documented test cases and test execution logs to be used as grounds for supporting testers' conclusion that a software product passed testing.

Another example is reporting a system failure. Regardless whether it is formal testing or unscripted exploratory testing, testers are required to document and report the defects they find. By reporting a defect, a tester first claims that a certain system feature failed testing and, second, presents an argument in the form of a defect description to support the claim. Such an argument should be logically valid to be sufficiently convincing for developers.

Deriving conclusions and presenting valid proofs, also known in mathematics as logical arguments, is frequently not a trivial matter. That is why mathematicians use deductive reasoning as a foundation for their strategies and techniques to derive conclusions and present valid arguments. Deductive reasoning is the type of reasoning used when deriving a conclusion from other sentences that are accepted as true [3]. As I discuss in this article, software testers can also benefit from using deductive reasoning. First, they can better understand the logic of software testing and, second, they can construct valid proofs better supporting their conclusions about product quality.

Applying Deductive Reasoning to Software Testing
In mathematics, the process of deriving a conclusion results in presenting a deductive argument or proof that is defined as a convincing argument that starts from the premises and logically deduces the desired conclusion. The proof theory discusses various logical patterns for deriving conclusions, called rules of inference , that are used as a basis for constructing valid arguments [2, 3]. An argument is said to be valid if the conclusion necessarily follows from its premise. Hence,


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