Highly automated vehicles (HAVs) are expected to fundamentally change the on-road transportation field by increasing traffic flow efficiency, reducing road crashes caused by human errors, and increasing comfort and driving productivity. With the help of recent developments in cognitive management techniques and machine learning analysis, intelligent on-board computing services are gaining acceptance. The main goal of the present paper is to introduce and develop a novel on-board cognitive decision-making functionality that dynamically and automatically enables HAVs to operate each time in the best available level of driving automation (LoDA). The proposed functionality utilizes several attributes associated with the driving environment and the driver's personality characteristics and personal preferences. The cognitive nature of the proposed functionality is based on previous knowledge, turned into experience, by implementing the Naive Bayes classifier supervised machine learning method. The effectiveness of the proposed cognitive functionality, in terms of accuracy and speed of convergence, in proactively identifying the optimal LoDA, is illustrated by modelling and analysing three scenarios with regards to drivers with different profile data and to driving scenes with different environment characteristics. Therefore, it can operate as an in-car intelligent personal assistant for the drivers.