Decision Trees with a Modal Flavor

Symbolic learning is the sub-field of machine learning that deals with symbolic algorithms and models, which have been known for decades and successfully applied to a variety of contexts, and of which decision trees are the quintessential expression. The main limitation of current symbolic models is the fact that they are essentially based on classical propositional logic, which implies that data with an implicit dimensional component, such as temporal, e.g., time series, or spatial data, e.g., images, cannot be properly dealt with within the standard symbolic framework. In this paper, we show how propositional logic in decision trees can be replaced with the more expressive (propositional) modal logics, and we lay down the formal bases of modal decision trees by first systematically delineating interesting and well-known properties of propositional ones and then showing how to transfer these properties to the modal case.