The abduction and consequence generation algorithm used by Logitest, a support system for logical MCQs designers

The design of multiple-choice questions (MCQs) to assess students’ knowledge and abilities is a delicate task. A well designed test is in fact required to meet some fundamental requirements, some concerning linguistic aspects and others being of a more logical nature. This paper presents a system that can be used to assist the designer of logical test items, i.e. questions aiming at verifying logical reasoning abilities (provided they can be represented in propositional logic). Beyond allowing the designer to check the status of an option with respect to the item stem (the problem presentation), i.e. whether it is derivable or consistent with the given information, the system can accomplish generative tasks (abduction and consequence generation) that can be useful both to complete the item stem, and to generate plausible distractors (incorrect options). The provably correct and complete algorithm used to perform abduction and consequence generation finds out minimal solutions without the need to compare each of them with all the others.