Decision Tree Learning with Spatial Modal Logics

Giovanni Pagliarini
(Dept. of Mathematics and Computer Science, University of Ferrara, Italy; Dept. of Mathematical, Physical and Computer Sciences, University of Parma, Italy)
Guido Sciavicco
(Dept. of Mathematics and Computer Science, University of Ferrara, Italy)

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.

In Pierre Ganty and Davide Bresolin: Proceedings 12th International Symposium on Games, Automata, Logics, and Formal Verification (GandALF 2021), Padua, Italy, 20-22 September 2021, Electronic Proceedings in Theoretical Computer Science 346, pp. 273–290.
This is partially dedicated to Alice.
Published: 17th September 2021.

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