  Symbolic learning represents the most straightforward approach to
interpretable modeling, but its applications have been hampered by a single
structural design choice: the adoption of propositional logic as the underlying
language. Recently, more-than-propositional symbolic learning methods have
started to appear, in particular for time-dependent data. These methods exploit
the expressive power of modal temporal logics in powerful learning algorithms,
such as temporal decision trees, whose classification capabilities are
comparable with the best non-symbolic ones, while producing models with
explicit knowledge representation.
  With the intent of following the same approach in the case of spatial data,
in this paper we: i) present a theory of spatial decision tree learning; ii)
describe a prototypical implementation of a spatial decision tree learning
algorithm based, and strictly extending, the classical C4.5 algorithm; and iii)
perform a series of experiments in which we compare the predicting power of
spatial decision trees with that of classical propositional decision trees in
several versions, for a multi-class image classification problem, on publicly
available datasets. Our results are encouraging, showing clear improvements in
the performances from the propositional to the spatial models, which in turn
show higher levels of interpretability.
