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Recent engineering developments have seen the emergence of Machine Learning(ML) as a powerful form of data analysis with widespread applicability beyondits historical roots in the design of autonomous agents. However, relativelylittle attention has been paid to the interaction between people and MLsystems. Recent developments on Explainable ML address this by providing visualand textual information on how the ML system arrived at a conclusion. In thispaper we view the interaction between humans and ML systems within the broadercontext of interaction between agents capable of learning and explanation.Within this setting, we argue that it is more helpful to view the interactionas characterised by two-way intelligibility of information rather than once-offexplanation of a prediction. We formulate two-way intelligibility as a propertyof a communication protocol. Development of the protocol is motivated by a setof `Intelligibility Axioms' for decision-support systems that use ML with ahuman-in-the-loop. The axioms are intended as sufficient criteria to claimthat: (a) information provided by a human is intelligible to an ML system; and(b) information provided by an ML system is intelligible to a human. The axiomsinform the design of a general synchronous interaction model between agentscapable of learning and explanation. We identify conditions of compatibilitybetween agents that result in bounded communication, and define Weak and StrongTwo-Way Intelligibility between agents as properties of the communicationprotocol.

A Protocol for Intelligible Interaction Between Agents That Learn and Explain