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2.3 From universal imitation to ORACLE

Universal imitation games distinguished static, dynamic, and evolutionary forms of imitation and contrasted inductive inference through initial algebras with coinductive inference through final coalgebras [ Mahadevan , 2024 ] . Their central move was to replace the recovery of a finite description by agreement with an indefinitely extensible behavioral presentation.

ORACLE retains that coinductive insight but removes the requirement that the unknown world already be presented as one fixed universal coalgebra. A final coalgebra is now one especially important target object in \(\mathfrak H_{\mathrm{core}}\), equipped with the corresponding agent interpretation. More generally, the learner may have to discover the objects, arrows, equations, information shapes, and universal constructions that make the observed behavior compositional at all.

The conceptual lineage. ORACLE generalizes coinductive discovery of a universal coalgebra to identification of an unknown categorical world. UOCL makes the identification process algorithmic; UODL adds a decision declaration to the learned predictive structure.
Figure 2.2 The conceptual lineage. ORACLE generalizes coinductive discovery of a universal coalgebra to identification of an unknown categorical world. UOCL makes the identification process algorithmic; UODL adds a decision declaration to the learned predictive structure.