Decision Tree Learning with Spatial Modal Logics

Abstract

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.

Evolutionary Explainable Rule Extraction from (Modal) Random Forests

“…The theoretical properties of ModalCART have been studied in [18]. Such an integration is particularly useful when ML is replaced by tailored temporal/spatial, but still modal, logic, as in [13,32,36], for specific learning tasks. The theoretical aspects of such integration, however, are independent from the particular modal logic used for learning; as a matter of fact, modal decision trees can be designed in the same way for any unary modal logic.…”

“…Modal logic, which extends propositional logic, can be adopted by decision trees as the underlying logical language, in order to capture complex relationships between objects and their properties, ultimately enabling models to learn from unstructured data with no feature-representation embedding steps (i.e., representing unstructured data as structured). Modal decision trees have been successfully used in complex tasks such as time series knowledge extraction, image understanding, and knowledge graph reasoning [13,32,36]. In the same spirit of canonical ones, branches of modal decision trees represent modal logic formulas.…”