We address the topic of specifying multi-agent systems using the situation and state calculus (SSC). SSC has been proposed as an extension of the situation calculus to overcome some limitations of the usual notion of state. The envisaged multiagent system specification framework allows the uniform treatment of both local and global properties, providing also techniques for reasoning about such specifications. When a certain intended property is not inferred from a specification, we cannot always just add to it the corresponding formula. Indeed, it is often the case that specification axioms are required to be formulae of a certain kind. The task of identifying the new axioms that should be added to the specification in order to ensure the intended property has an abductive nature. Herein, we develop abductive reasoning techniques to tackle this problem.