Abstract
This paper presents a logical Style painting classifier based on evaluated Horn clauses, qualitative colour descriptors and Explanations ($\ell $-SHE). Three versions of $\ell $-SHE are defined, using rational Pavelka logic (RPL), and expansions of Gödel logic and product logic with rational constants: RPL, $G(\mathbb{Q})$ and $\sqcap (\mathbb{Q})$, respectively. We introduce a fuzzy representation of the more representative colour traits for the Baroque, the Impressionism and the Post-Impressionism art styles. The $\ell $-SHE algorithm has been implemented in Swi-Prolog and tested on 90 paintings of the QArt-Dataset and on 247 paintings of the Paintings-91-PIB dataset. The percentages of accuracy obtained in the QArt-Dataset for each $\ell $-SHE version are 73.3% (RPL), 65.6% ($G(\mathbb{Q})$) and 68.9% ($\sqcap (\mathbb{Q})$). Regarding the Paintings-91-PIB dataset, the percentages of accuracy obtained for each $\ell $-SHE version are 60.2% (RPL), 48.2% ($G(\mathbb{Q})$) and 57.0% ( $\sqcap (\mathbb{Q})$). Our logic definition for the Baroque style has obtained the highest accuracy in both datasets, for all the $\ell $-SHE versions (the lowest Baroque case gets 85.6$\%$ of accuracy). An important feature of the classifier is that it provides reasons regarding why a painting belongs to a certain style. The classifier also provides reasons about why outliers of one art style may belong to another art style, giving a second classification option depending on its membership degrees to these styles.
An Algebraic Study of S5-Modal Gödel Logic
