# Decision Tree Learning with Spatial Modal Logics

arXiv: https://arxiv.org/abs/2109.08325 · HTML: https://mlsanity.com/paper/2109.08325/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 54 references that are in the map.
- First posted on arXiv 17 Sep 2021.

## Builds on (most cited first, 7 of 7)

- [HybridSN: Exploring 3D-2D CNN Feature Hierarchy for Hyperspectral Image Classification](https://mlsanity.com/paper/1902.06701/) (2019)
- [Deep Learning for Classification of Hyperspectral Data: A Comparative Review](https://mlsanity.com/paper/1904.10674/) (2019)
- [Hyperspectral Image Classification with Markov Random Fields and a Convolutional Neural Network](https://mlsanity.com/paper/1705.00727/) (2017)
- [Interval Temporal Logic Decision Tree Learning](https://mlsanity.com/paper/2003.04952/) (2020)
- [BASS Net: Band-Adaptive Spectral-Spatial Feature Learning Neural Network for Hyperspectral Image Classification](https://mlsanity.com/paper/1612.00144/) (2016)
- [Horn Fragments of the Halpern-Shoham Interval Temporal Logic (Technical Report)](https://mlsanity.com/paper/1604.03515/) (2016)
- [Hyperspectral Image Classification with Deep Metric Learning and Conditional Random Field](https://mlsanity.com/paper/1903.06258/) (2019)

## Abstract (arXiv)

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.