Fig. 4. Qualitative results on morpho-phonological grammar discovery illustrated on phonology textbook problems.

The model observes form/meaning pairs (orange) and jointly infers both a language-specific theory (teal; phonological rules labeled r₁, r₂, ...) and a data set-specific lexicon (teal) containing stems and affixes. Together the theory and lexicon explain the orange data via a derivation where the morphology output (prefix+stem+suffix) is transformed according to the ordered rules. Notice interacting nonlocal rules in Kerewe, a language with tones. Notice multiple vowel harmony rules in Sakha. Supplementary Figs. 1–3 provide analogous illustrations of grammars with epenthesis (Yowlumne), stress (Serbo-Croatian), vowel harmony (Turkish, Hungarian, Yowlumne), assimilation (Lumasaaba), and representative partial failure cases on Yowlumne and Somali (where it recovers a partly correct rule set that fails to explain 20% of the data, while also illustrating spirantization).