Generating Quantifiers and Negation to Explain Homework Testing

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The authors describe Prograder, a software package for automatic checking of requirements for programming homework assignments. Prograder lets instructors specify requirements in natural language as well as explains grading results to students in natural language. It does so using a grammar that generates as well as parses to translate between a small fragment of English and a first-order logical specification language that can be executed directly in Python. This execution embodies multiple semantics - both to check the requirement and to search for evidence that proves or disproves the requirement. Such a checker needs to interpret and generate sentences containing quantifiers and negation.